Sample records for geometric transitions topological

Mirror symmetry is one of the most beautiful symmetries in string theory. It helps us very effectively gain insights into non-perturbative worldsheet instanton effects. It was also shown that the study of mirror symmetry for Calabi-Yau flux compactification leads us to the territory of ''Non-Kaehlerity''. In this thesis we demonstrate how to construct a new class of symplectic non-Kaehler and complex non-Kaehler string theory vacua via generalized geometrictransitions. The class admits a mirror pairing by construction. From a variety of sources, including super-gravity analysis and KK reduction on SU(3) structure manifolds, we conclude that string theory connects Calabi-Yau spaces to both complex non-Kaehler and symplectic non-Kaehler manifolds and the resulting manifolds lie in generalized complex geometry. We go on to study the topological twisted models on a class of generalized complex geometry, bi-Hermitian geometry, which is the most general target space for (2, 2) world-sheet theory with non-trivial H flux turned on. We show that the usual Kaehler A and B models are generalized in a natural way. Since the gauged supergravity is the low energy effective theory for the compactifications on generalized geometries, we study the fate of flux-induced isometry gauging in N = 2 IIA and heterotic strings under non-perturbative instanton effects. Interestingly, we find we have protection mechanisms preventing the corrections to the hyper moduli spaces. Besides generalized geometries, we also discuss the possibility of new NS-NS fluxes in a new doubled formalism.

Geometry, both in momentum and in real space, plays an important role in the electronic dynamics of condensed matter systems. Among them, the Berry phase associated with nontrivial geometry can be an origin of the transverse motion of electrons, giving rise to various geometric effects such as the anomalous, spin and topological Hall effects. Here, we report two unconventional manifestations of Hall physics: a sign-reversal of the anomalous Hall effect, and the emergence of a topological Hall effect in magnetic/non-magnetic topological insulator heterostructures, Crx(Bi1-ySby)2-xTe3/(Bi1-ySby)2Te3. The sign-reversal in the anomalous Hall effect is driven by a Rashba splitting at the bulk bands, which is caused by the broken spatial inversion symmetry. Instead, the topological Hall effect arises in a wide temperature range below the Curie temperature, in a region where the magnetic-field dependence of the Hall resistance largely deviates from the magnetization. Its origin is assigned to the formation of a Néel-type skyrmion induced by the Dzyaloshinskii-Moriya interaction.

Spatial computing is an emerging field that recognizes the importance of explicitly handling spatial relationships at three levels: computer architectures, programming languages and applications. In this context, we present MGS, an experimental programming language where data structures are fields on abstract spaces. In MGS, fields are transformed using rules. We show that this approach is able to unify, at least for programming purposes, several computational models like Lindenmayer systems and cellular automata. The MGS notions of topological collection and transformation are formalized using concepts developed in algebraic topology. We propose to use transformations in order to implement a discrete version of some differential operators. These transformations satisfy a Stokes-like theorem. This result constitutes a geometric view of programming where data are handled like fields in physics. The relevance of this approach for the design of autonomic software systems is discussed in the conclusion.

The fractional quantum Hall (FQH) effect illustrates the range of novel phenomena which can arise in a topologically ordered state in the presence of strong interactions. The possibility of realizing FQH-like phases in models with strong lattice effects has attracted intense interest as a more experimentally accessible venue for FQH phenomena which calls for more theoretical attention. Here we investigate the physical relevance of previously derived geometric conditions which quantify deviations from the Landau level physics of the FQHE. We conduct extensive numerical many-body simulations on several lattice models, obtaining new theoretical results in the process, and find remarkable correlation between these conditions and the many-body gap. These results indicate which physical factors are most relevant for the stability of FQH-like phases, a paradigm we refer to as the geometric stability hypothesis, and provide easily implementable guidelines for obtaining robust FQH-like phases in numerical or real-world experiments. PMID:26530311

The octree technique is developed into the finite octree, and an overview is given. Modeler requirements are given. The octree discretization is discussed along with geometric communication operators. Geometric communication operators returning topological associativity and geometric communication operators returning spatial data are also discussed and illustrated. The advantages are given of the boundary representation and of geometric communication operators. The implementation plays an important role in the integration with a variety of geometric modelers. The capabilities of closed loop processes within a complete finite element system are presented.

Induced by the Hagedorn instability, weakly-coupled U (N) gauge theories on a compact manifold exhibit a confinement/deconfinement phase transition in the large-N limit. Recently we discover that the thermal entropy of a free theory on S3 gets reduced by a universal constant term, -N2 / 4, compared to that from completely deconfined colored states. This entropy deficit is due to the persistence of Gauss's law, and actually independent of the shape of the manifold. In this paper we show that this universal term can be identified as the topological entangle entropy both in the corresponding 4 + 1 D bulk theory and the dimensionally reduced theory. First, entanglement entropy in the bulk theory contains the so-called "particle" contribution on the entangling surface, which naturally gives rise to an area-law term. The topological term results from the Gauss's constraint of these surface states. Secondly, the high-temperature limit also defines a dimensionally reduced theory. We calculate the geometric entropy in the reduced theory explicitly, and find that it is given by the same constant term after subtracting the leading term of O (β-1). The two procedures are then applied to the confining phase, by extending the temperature to the complex plane. Generalizing the recently proposed 2D modular description to an arbitrary matter content, we show the leading local term is missing and no topological term could be definitely isolated. For the special case of N = 4 super Yang-Mills theory, the results obtained here are compared with that at strong coupling from the holographic derivation.

We develop a theory of topologicaltransitions in a Floquet topological insulator, using graphene irradiated by circularly polarized light as a concrete realization. We demonstrate that a hallmark signature of such transitions in a static system, i.e., metallic bulk transport with conductivity of order e^{2}/h, is substantially suppressed at some Floquet topologicaltransitions in the clean system. We determine the conditions for this suppression analytically and confirm our results in numerical simulations. Remarkably, introducing disorder dramatically enhances this transport by several orders of magnitude. PMID:25526148

We develop a theory of topologicaltransitions in a Floquet topological insulator, using graphene irradiated by circularly polarized light as a concrete realization. We demonstrate that a hallmark signature of such transitions in a static system, i.e., metallic bulk transport with conductivity of order e2/h , is substantially suppressed at some Floquet topologicaltransitions in the clean system. We determine the conditions for this suppression analytically and confirm our results in numerical simulations. Remarkably, introducing disorder dramatically enhances this transport by several orders of magnitude.

Detecting meaningful structure in neural activity and connectivity data is challenging in the presence of hidden nonlinearities, where traditional eigenvalue-based methods may be misleading. We introduce a novel approach to matrix analysis, called clique topology, that extracts features of the data invariant under nonlinear monotone transformations. These features can be used to detect both random and geometric structure, and depend only on the relative ordering of matrix entries. We then analyzed the activity of pyramidal neurons in rat hippocampus, recorded while the animal was exploring a 2D environment, and confirmed that our method is able to detect geometric organization using only the intrinsic pattern of neural correlations. Remarkably, we found similar results during nonspatial behaviors such as wheel running and rapid eye movement (REM) sleep. This suggests that the geometric structure of correlations is shaped by the underlying hippocampal circuits and is not merely a consequence of position coding. We propose that clique topology is a powerful new tool for matrix analysis in biological settings, where the relationship of observed quantities to more meaningful variables is often nonlinear and unknown. PMID:26487684

When modeling deformation of geometrically complex regions, unstructured tetrahedral meshes provide the flexibility necessary to track interfaces as they change geometrically and topologically. In the class of time-dependent simulations considered in this paper, multimaterial interfaces are represented by sets of triangular facets, and motion of the interfaces is controlled by physical considerations. The motion of interior points in the conforming tetrahedral mesh (i.e., points not on interfaces) is arbitrary and may be chosen to produce good element shapes. In the context of specified boundary motion driven by physical considerations, they have found that a rather large glossary of mesh changes is required to allow the simulation to survive all the transitions of interface geometry and topology that occur during time evolution. This paper will describe mesh changes required to maintain good element quality as the geometry evolves, as well as mesh changes required to capture changes i n topology that occur when material regions collapse or pinch off. This paper will present a detailed description of mesh changes necessary for capturing the aforementioned geometrical and topological changes, as implemented in the code GRAIN3D, and will provide examples from a metallic grain growth simulation in which the normal velocity of the grain boundary is proportional to mean curvature.

Topology, with its abstract mathematical constructs, often manifests itself in physics and has a pivotal role in our understanding of natural phenomena. Notably, the discovery of topological phases in condensed-matter systems has changed the modern conception of phases of matter. The global nature of topological ordering, however, makes direct experimental probing an outstanding challenge. Present experimental tools are mainly indirect and, as a result, are inadequate for studying the topology of physical systems at a fundamental level. Here we employ the exquisite control afforded by state-of-the-art superconducting quantum circuits to investigate topological properties of various quantum systems. The essence of our approach is to infer geometric curvature by measuring the deflection of quantum trajectories in the curved space of the Hamiltonian. Topological properties are then revealed by integrating the curvature over closed surfaces, a quantum analogue of the Gauss-Bonnet theorem. We benchmark our technique by investigating basic topological concepts of the historically important Haldane model after mapping the momentum space of this condensed-matter model to the parameter space of a single-qubit Hamiltonian. In addition to constructing the topological phase diagram, we are able to visualize the microscopic spin texture of the associated states and their evolution across a topological phase transition. Going beyond non-interacting systems, we demonstrate the power of our method by studying topology in an interacting quantum system. This required a new qubit architecture that allows for simultaneous control over every term in a two-qubit Hamiltonian. By exploring the parameter space of this Hamiltonian, we discover the emergence of an interaction-induced topological phase. Our work establishes a powerful, generalizable experimental platform to study topological phenomena in quantum systems.

Topology, with its abstract mathematical constructs, often manifests itself in physics and has a pivotal role in our understanding of natural phenomena. Notably, the discovery of topological phases in condensed-matter systems has changed the modern conception of phases of matter. The global nature of topological ordering, however, makes direct experimental probing an outstanding challenge. Present experimental tools are mainly indirect and, as a result, are inadequate for studying the topology of physical systems at a fundamental level. Here we employ the exquisite control afforded by state-of-the-art superconducting quantum circuits to investigate topological properties of various quantum systems. The essence of our approach is to infer geometric curvature by measuring the deflection of quantum trajectories in the curved space of the Hamiltonian. Topological properties are then revealed by integrating the curvature over closed surfaces, a quantum analogue of the Gauss-Bonnet theorem. We benchmark our technique by investigating basic topological concepts of the historically important Haldane model after mapping the momentum space of this condensed-matter model to the parameter space of a single-qubit Hamiltonian. In addition to constructing the topological phase diagram, we are able to visualize the microscopic spin texture of the associated states and their evolution across a topological phase transition. Going beyond non-interacting systems, we demonstrate the power of our method by studying topology in an interacting quantum system. This required a new qubit architecture that allows for simultaneous control over every term in a two-qubit Hamiltonian. By exploring the parameter space of this Hamiltonian, we discover the emergence of an interaction-induced topological phase. Our work establishes a powerful, generalizable experimental platform to study topological phenomena in quantum systems. PMID:25391961

We show that the physics of D-brane theories that exhibit dynamical SUSY breaking due to stringy instanton effects is well captured by geometrictransitions, which recast the non-perturbative superpotential as a classical flux superpotential. This allows for simple engineering of Fayet, Polonyi, O'Raifeartaigh, and other canonical models of supersymmetry breaking in which an exponentially small scale of breaking can be understood either as coming from stringy instantons or as arising from the classical dynamics of fluxes.

Topological aspect of the geometric phase (GP) due to pure polarization projection is studied using the 2D Fourier transform (2D-FT) method. Projection of orthogonal polarization state results in a phase singularity in the 2D parameter space of ellipticity and orientation of polarization ellipse. Projection of its surrounding states results in an accumulation of GP in different amount that form a spiral structure. A half wave plate–quarter wave plate combination is used to generate different polarization states which are projected using a polarizer. The accumulated phase for each orientation of the wave plate is extracted from 2D-FT of the interferogram, obtained by interfering it with a reference beam in a Mach–Zehnder like interferometer.

Finite element meshes derived automatically from solid models through recursive spatial subdivision schemes (octrees) can be made to inherit the hierarchical structure and the spatial addressability intrinsic to the underlying grid. These two properties, together with the geometric regularity that can also be built into the mesh, make octree based meshes ideally suited for efficient analysis and self-adaptive remeshing and reanalysis. The element decomposition of the octal cells that intersect the boundary of the domain is discussed. The problem, central to octree based meshing, is solved by combining template mapping and element extraction into a procedure that utilizes both constructive solid geometry and boundary representation techniques. Boundary cells that are not intersected by the edge of the domain boundary are easily mapped to predefined element topology. Cells containing edges (and vertices) are first transformed into a planar polyhedron and then triangulated via element extractor. The modeling environments required for the derivation of planar polyhedra and for element extraction are analyzed.

Systems with holes, such as colloidal handlebodies and toroidal droplets, have been studied in the nematic liquid crystal (NLC) 4-cyano-4'-pentylbiphenyl (5CB): Both point and ring topological defects can occur within each hole and around the system while conserving the system's overall topological charge. However, what has not been fully appreciated is the ability to manipulate the hole geometry with homeotropic (perpendicular) anchoring conditions to induce complex, saddle-like deformations. We exploit this by creating an array of holes suspended in an NLC cell with oriented planar (parallel) anchoring at the cell boundaries. We study both 5CB and a binary mixture of bicyclohexane derivatives (CCN-47 and CCN-55). Through simulations and experiments, we study how the bulk saddle deformations of each hole interact to create defect structures, including an array of disclination lines, reminiscent of those found in liquid-crystal blue phases. The line locations are tunable via the NLC elastic constants, the cell geometry, and the size and spacing of holes in the array. This research lays the groundwork for the control of complex elastic deformations of varying length scales via geometrical cues in materials that are renowned in the display industry for their stability and easy manipulability. PMID:27222582

The form and shape of a hypothesis space imposes natural objective constraints to any inferential process. This contribution summarizes what is currently known and the mathematics that are thought to be needed for new developments in this area. For example, it is well known that the quality of best possible estimators deteriorates with increasing volume, dimension and curvature of the hypothesis space. It is also known that regular statistical parametric models are finite dimensional Riemannian manifolds admitting a family of dual affine connections. Fisher information is the metric induced on the hypothesis space by the Hellinger distance. Nonparametric models are infinite dimensional manifolds. Global negative curvature implies asymptotic inadmissibility of uniform priors. When there is uncertainty about the model and the prior, entropic methods are more robust than standard Bayesian inference. The presence of some types of singularities allow the existence of faster than normal estimators …, etc. The large number of fundamental statistical concepts with geometric and topological content suggest to try to look at Riemannian Geometry, Algebraic Geometry, K-theory, Algebraic Topology, Knot-theory and other branches of current mathematics, not as empty esoteric abstractions but as allies for statistical inference.

Despite considerable interest in layered transition metal dichalcogenides (TMDs), such as M X2 with M =(Mo ,W ) and X =(S ,Se ,Te ) , the physical origin of their topological nature is still poorly understood. In the conventional view of topological phase transition (TPT), the nontrivial topology of electron bands in TMDs is caused by the band inversion between metal d - and chalcogen p -orbital bands where the former is pulled down below the latter. Here, we show that, in TMDs, the TPT is entirely different from the conventional speculation. In particular, M S2 and M S e2 exhibits the opposite behavior of TPT such that the chalcogen p -orbital band moves down below the metal d -orbital band. More interestingly, in M T e2 , the band inversion occurs between the metal d -orbital bands. Our findings cast doubts on the common view of TPT and provide clear guidelines for understanding the topological nature in new topological materials to be discovered.

The continuous quantum phase transition between noninteracting, time-reversal symmetric topological and trivial insulators in three dimensions is described by the massless Dirac fermion. We address the stability of this quantum critical point against short range electronic interactions by using renormalization group analysis and mean field theory. For sufficiently weak interactions, we show that the nature of the direct transition remains unchanged. Beyond a critical strength of interactions we find that either (i) there is a direct first order transition between two time reversal symmetric insulators or (ii) the direct transition is eliminated by an intervening time reversal and inversion odd "axionic" insulator. We also demonstrate the existence of an interaction driven first order quantum phase transition between topological and trivial gapped states in lower dimensions.

Topologically ordered systems are characterized by topological invariants that are often calculated from the momentum space integration of a certain function that represents the curvature of the many-body state. The curvature function may be Berry curvature, Berry connection, or other quantities depending on the system. Akin to stretching a messy string to reveal the number of knots it contains, a scaling procedure is proposed for the curvature function in inversion symmetric systems, from which the topological phase transition can be identified from the flow of the driving energy parameters that control the topology (hopping, chemical potential, etc) under scaling. At an infinitesimal operation, one obtains the renormalization group (RG) equations for the driving energy parameters. A length scale defined from the curvature function near the gap-closing momentum is suggested to characterize the scale invariance at critical points and fixed points, and displays a universal critical behavior in a variety of systems examined. PMID:26790004

We study the nonequilibrium time evolution of a variety of one-dimensional (1D) and two-dimensional (2D) systems (including SSH model, Kitaev-chain, Haldane model, p +i p superconductor, etc.) following a sudden quench. We prove analytically that topology-changing quenches are always followed by nonanalytical temporal behavior of return rates (logarithm of the Loschmidt echo), referred to as dynamical phase transitions (DPTs) in the literature. Similarly to edge states in topological insulators, DPTs can be classified as being topologically protected or not. In 1D systems the number of topologically protected nonequilibrium time scales are determined by the difference between the initial and final winding numbers, while in 2D systems no such relation exists for the Chern numbers. The singularities of dynamical free energy in the 2D case are qualitatively different from those of the 1D case; the cusps appear only in the first time derivative.

In this paper, we prove that for any f∈Diff1 (M) and Λ ⊂ M be a nontrivial topologicallytransitive proper subset with a splitting Es ⊕ F (without hypothesis of domination), where Es is uniformly contracting, there is no arc of the stable manifold whole contained in Λ.

Topological phase transition is accompanied with a change of topological numbers. According to the bulk-edge correspondence, the gap closing and the breakdown of the adiabaticity are necessary at the phase transition point to make the topological number ill-defined. However, the gap closing is not always needed. In this paper, we show that two topological distinct phases can be continuously connected without gap closing, provided the symmetry of the system changes during the process. Here we propose the generic principles how this is possible by demonstrating various examples such as 1D polyacetylene with the charge-density-wave order, 2D silicene with the antiferromagnetic order, 2D silicene or quantum well made of HgTe with superconducting proximity effects and 3D superconductor Cu doped Bi2Se3. It is argued that such an unusual phenomenon can occur when we detour around the gap closing point provided the connection of the topological numbers is lost along the detour path. PMID:24071900

Topologicaltransitions in bubbling half-BPS Type IIB geometries with SO(4) x SO(4) symmetry can be decomposed into a sequence of n elementary transitions. The half-BPS solution that describes the elementary transition is seeded by a phase space distribution of fermions filling two diagonal quadrants. We study the geometry of this solution in some detail. We show that this solution can be interpreted as a time dependent geometry, interpolating between two asymptotic pp-waves in the far past and the far future. The singular solution at the transition can be resolved in two different ways, related by the particle-hole duality in the effective fermion description. Some universal features of the topology change are governed by two-dimensional Type 0B string theory, whose double scaling limit corresponds to the Penrose limit of AdS_5 x S^5 at topologicaltransition. In addition, we present the full class of geometries describing the vicinity of the most general localized classical singularity that can occur in this class of half-BPS bubbling geometries.

Topologicaltransitions in bubbling half-BPS Type IIB geometries with SO(4) x SO(4) symmetry can be decomposed into a sequence of n elementary transitions. The half-BPS solution that describes the elementary transition is seeded by a phase space distribution of fermions filling two diagonal quadrants. We study the geometry of this solution in some detail. We show that this solution can be interpreted as a time dependent geometry, interpolating between two asymptotic pp-waves in the far past and the far future. The singular solution at the transition can be resolved in two different ways, related by the particle-hole duality in the effective fermion description. Some universal features of the topology change are governed by two-dimensional Type 0B string theory, whose double scaling limit corresponds to the Penrose limit of AdS_5 x S5 at topologicaltransition. In addition, we present the full class of geometries describing the vicinity of the most general localized classical singularity that can occur in this class of half-BPS bubbling geometries.

Despite considerable interests in transition metal dichalcogenides (TMDs), such as MX2 with M = (Mo, W) and X = (S, Se, Te), the physical origin of their topological nature is still in its infancy. The conventional view of topological phase transition (TPT) in TMDs is that the band inversion occurs between the metal d and chalcogen p orbital bands. More precisely, the former is pulled down below the latter. Here we introduce an explicit scheme for analyzing TPT in topological materials and find that the TPT in TMDs is different from the conventional speculation. When the 1T phase undergoes a structural transformation to the 1T' phase in monolayer MX2, the band topology changes from trivial to non-trivial, leading to the TPT. We discuss the exact role of the metal d and chalcogen p orbital bands during the TPT. Our finding would provide clear guidelines for understanding the topological nature not only in TMDs but also in other topological materials yet to be explored.

A Josephson junction formed by a superconducting ring interrupted by a semiconductor nanowire can realize a zero-dimensional class D topological superconductor. By coupling the Josephson junction to a ballistic wire and altering the strength of the coupling, one can drive this topological superconductor through a topological phase transition. We study the compressibility of the junction as a probe of the topological phase transition. We also study the dynamics of the phase transition by studying the current pulse injected into the wire.

Topological insulators and topological superconductors are distinguished by their bulk phase transitions and gapless states at a sharp boundary with the vacuum. Quasicrystals have recently been found to be topologically nontrivial. In quasicrystals, the bulk phase transitions occur in the same manner as standard topological materials, but their boundary phenomena are more subtle. In this Letter we directly observe bulk phase transitions, using photonic quasicrystals, by constructing a smooth boundary between topologically distinct one-dimensional quasicrystals. Moreover, we use the same method to experimentally confirm the topological equivalence between the Harper and Fibonacci quasicrystals. PMID:25166388

Extracting useful information from large data sets can be a daunting task. Topological methods for analysing data sets provide a powerful technique for extracting such information. Persistent homology is a sophisticated tool for identifying topological features and for determining how such features persist as the data is viewed at different scales. Here we present quantum machine learning algorithms for calculating Betti numbers--the numbers of connected components, holes and voids--in persistent homology, and for finding eigenvectors and eigenvalues of the combinatorial Laplacian. The algorithms provide an exponential speed-up over the best currently known classical algorithms for topological data analysis. PMID:26806491

Extracting useful information from large data sets can be a daunting task. Topological methods for analysing data sets provide a powerful technique for extracting such information. Persistent homology is a sophisticated tool for identifying topological features and for determining how such features persist as the data is viewed at different scales. Here we present quantum machine learning algorithms for calculating Betti numbers--the numbers of connected components, holes and voids--in persistent homology, and for finding eigenvectors and eigenvalues of the combinatorial Laplacian. The algorithms provide an exponential speed-up over the best currently known classical algorithms for topological data analysis.

Extracting useful information from large data sets can be a daunting task. Topological methods for analysing data sets provide a powerful technique for extracting such information. Persistent homology is a sophisticated tool for identifying topological features and for determining how such features persist as the data is viewed at different scales. Here we present quantum machine learning algorithms for calculating Betti numbers—the numbers of connected components, holes and voids—in persistent homology, and for finding eigenvectors and eigenvalues of the combinatorial Laplacian. The algorithms provide an exponential speed-up over the best currently known classical algorithms for topological data analysis. PMID:26806491

At the interface of an s -wave superconductor and a three-dimensional topological insulator, Majorana zero modes and Majorana helical states have been proposed to exist respectively around magnetic vortices and geometrical edges. Here we first show that randomly distributed magnetic impurities at such an interface will induce bound states that broaden into impurity bands inside (but near the edges of) the superconducting gap, which remains open unless the impurity concentration is too high. Next we find that an increase in the superconducting gap suppresses both the oscillation magnitude and the period of the Ruderman-Kittel-Kasuya-Yosida interaction between two magnetic impurities. Within a mean-field approximation, the ferromagnetic Curie temperature is found to be essentially independent of the superconducting gap, an intriguing phenomenon due to a compensation effect between the short-range ferromagnetic and long-range antiferromagnetic interactions. The existence of robust superconductivity and persistent ferromagnetism at the interface allows realization of a novel topological phase transition from a nonchiral to a chiral superconducting state at sufficiently low temperatures, providing a new platform for topological quantum computation.

Efforts aimed at large-scale integration of nanoelectronic devices that exploit the superior electronic and mechanical properties of single-walled carbon nanotubes (SWCNTs) remain limited by the difficulties associated with manipulation and packaging of individual SWNTs. Alternative approaches based on ultrathin carbon nanotube networks (CNNs) have enjoyed success of late with the realization of several scalable device applications. However, precise control over the network electronic transport is challenging due to (i) an often uncontrollable interplay between network coverage and its detailed topology and (ii) the inherent electrical heterogeneity of the constituent SWNTs. In this article, we use template-assisted fluidic assembly of SWCNT networks to explore the effect of geometric confinement on the network topology. Heterogeneous SWCNT networks dip-coated onto submicrometer wide ultrathin polymer channels become increasingly aligned with decreasing channel width and thickness. Experimental-scale coarse-grained computations of interacting SWCNTs show that the effect is a reflection of a topology that is no longer dependent on the network density, which in turn emerges as a robust knob that can induce semiconductor-to-metallic transitions in the network response. Our study demonstrates the effectiveness of directed assembly on channels with varying degrees of confinement as a simple tool to tailor the conductance of the otherwise heterogeneous network, opening up the possibility of robust large-scale CNN-based devices. PMID:20695518

Since the establishment of Darcy's law, analysis of porous-media flows has focused primarily on linking macroscopic transport properties, such as mean flow rate and dispersion, to the pore statistics of the material matrix. Despite intense efforts to understand the fluid velocity statistics from the porous-media structure, a qualitative and quantitative connection remains elusive. Here, we combine precisely controlled experiments with theory to quantify how geometric disorder in the matrix affects the flow statistics and transport in a quasi-2D microfluidic channel. Experimentally measured velocity fields for a range of different microstructure configurations are found to be in excellent agreement with large-scale numerical simulations. By successively increasing the matrix disorder, we study the transition from periodic flow structures to transport networks consisting of extended high-velocity channels. Morse-Smale complex analysis of the flow patterns reveals a topological phase transition that is linked to a qualitative change in the physical transport properties. This work demonstrates that topological flow analysis provides a mathematically well-defined, broadly applicable framework for understanding and quantifying fluid transport in complex geometries.

We consider a gapped periodic quantum system with time-reversal symmetry of fermionic (or odd) type, i.e. the time-reversal operator squares to -1. We investigate the existence of periodic and time-reversal invariant Bloch frames in dimensions 2 and 3. In 2 d, the obstruction to the existence of such a frame is shown to be encoded in a Z_2-valued topological invariant, which can be computed by a simple algorithm. We prove that the latter agrees with the Fu-Kane index. In 3 d, instead, four Z_2 invariants emerge from the construction, again related to the Fu-Kane-Mele indices. When no topological obstruction is present, we provide a constructive algorithm yielding explicitly a periodic and time-reversal invariant Bloch frame. The result is formulated in an abstract setting, so that it applies both to discrete models and to continuous ones.

Weyl semimetals are semimetals with nondegenerate 3D Dirac cones in the bulk. We showed that in a transition between different Z2 topological phases, i.e. between the normal insulator (NI) and topological insulator (TI), the Weyl semimetal phase necessarily appears when inversion symmetry is broken. In the presentation we show that this scenario holds for materials with any space groups without inversion symmetry. Namely, let us take any band insulator without inversion symmetry, and assume that the gap is closed by a change of an external parameter. In such cases we found that the system runs either into (i) a Weyl semimetal or (ii) a nodal-line semimetal, but no insulator-to-insulator transition happens. This is confirmed by classifying the gap closing in terms of the space groups and the wavevector. In the case (i), the number of Weyl nodes produced at the gap closing ranges from 2 to 12 depending on the symmetry. In (ii) the nodal line is protected by mirror symmetry. In the presentation, we explain some Weyl semimetal and nodal-line semimetals which we find by using this classification. As an example, we explain our result on ab initio calculation on tellurium (Te). Tellurium consists of helical chains, and therefore lacks inversion and mirror symmetries. At high pressure the band gap of Te decreases and finally it runs into a Weyl semimetal phase, as confirmed by our ab initio calculation. In such chiral systems as tellurium, we also theoretically propose chiral transport in systems with such helical structures; namely, an orbital magnetization is induced by a current along the chiral axis, in analogy with a solenoid.

Typically, structural topology optimization problems undergo relaxation of certain design parameters to allow the existence of intermediate variable optimum topologies. Relaxation permits the use of a variety of gradient-based search techniques and has been shown to guarantee the existence of optimal solutions and eliminate mesh dependencies. This Technical Publication (TP) will demonstrate the application of relaxation to a control point discretization of the design workspace for the structural topology optimization process. The control point parameterization with subdivision has been offered as an alternative to the traditional method of discretized finite element design domain. The principle of relaxation demonstrates the increased utility of the control point parameterization. One of the significant results of the relaxation process offered in this TP is that direct manufacturability of the optimized design will be maintained without the need for designer intervention or translation. In addition, it will be shown that relaxation of certain parameters may extend the range of problems that can be addressed; e.g., in permitting limited out-of-plane motion to be included in a path generation problem.

One-dimensional models with topological band structures represent a simple and versatile platform to demonstrate novel topological concepts. Here we experimentally study topologically protected states in silicon at the interface between two dimer chains with different Zak phases. Furthermore, we propose and demonstrate that, in a system where topological and trivial defect modes coexist, we can probe them independently. Tuning the configuration of the interface, we observe the transition between a single topological defect and a compound trivial defect state. These results provide a new paradigm for topologically protected waveguiding in a complementary metal-oxide-semiconductor compatible platform and highlight the novel concept of isolating topological and trivial defect modes in the same system that can have important implications in topological physics. PMID:27152805

The evolution of many kinetic processes in 1+1 (space-time) dimensions results in 2 D directed percolative landscapes. The active phases of these models possess numerous hidden geometric orders characterized by various types of large-scale and/or coarse-grained percolative backbones that we define. For the patterns originated in the classical directed percolation (DP) and contact process we show from the Monte Carlo simulation data that these percolative backbones emerge at specific critical points as a result of continuous phase transitions. These geometrictransitions belong to the DP universality class and their nonlocal order parameters are the capacities of corresponding backbones. The multitude of conceivable percolative backbones implies the existence of infinite cascades of such geometrictransitions in the kinetic processes considered. We present simple arguments to support the conjecture that such cascades of transitions are a generic feature of percolation as well as of many other transitions with nonlocal order parameters.

The evolution of many kinetic processes in 1+1 (space-time) dimensions results in 2D directed percolative landscapes. The active phases of these models possess numerous hidden geometric orders characterized by various types of large-scale and/or coarse-grained percolative backbones that we define. For the patterns originated in the classical directed percolation (DP) and contact process we show from the Monte Carlo simulation data that these percolative backbones emerge at specific critical points as a result of continuous phase transitions. These geometrictransitions belong to the DP universality class and their nonlocal order parameters are the capacities of corresponding backbones. The multitude of conceivable percolative backbones implies the existence of infinite cascades of such geometrictransitions in the kinetic processes considered. We present simple arguments to support the conjecture that such cascades of transitions are a generic feature of percolation as well as of many other transitions with nonlocal order parameters. PMID:26871019

We consider two-dimensional Chern insulators and time-reversal invariant topological insulators and discuss the effect of perturbations breaking either particle-number conservation or time-reversal symmetry. The appearance of trivial mass terms is expected to cause quantum phase transitions into trivial phases when such a perturbation overweighs the topological term. These phase transitions are usually associated with a bulk-gap closing. In contrast, the chiral Chern insulator is unaffected by particle-number breaking perturbations. Moreover, the [Formula: see text] topological insulator undergoes phase transitions into topologically trivial phases without bulk-gap closing in the presence of any of such perturbations. In certain cases, these phase transitions can be circumvented and the protection restored by another U(1) symmetry, e.g. due to spin conservation. These findings are discussed in the context of interacting topological insulators. PMID:27530509

We explore topological phase transition, which involves the energy spectra of field-induced spin-density-wave (FISDW) states in quasi-one dimensional (Q1D) organic conductors, using an extended Su-Schrieffer-Heeger (SSH) model. We show that, in presence of half magnetic-flux FISDW state, the system exhibits topologically nontrivial phases, which can be characterized by a nonzero Chern number. The nontrivial evolution of the bulk bands with chemical potential in a topological phase transition is discussed. We show that the system can have a similar phase diagram which is discussed in the Haldane’s model. We suggest that the topological feature should be tested experimentally in this organic system. These studies enrich the theoretical research on topologically nontrivial phases in the Q1D lattice system as compared to the Haldane topological phase appearing in the two-dimensional lattices. PMID:26612317

We explore topological phase transition, which involves the energy spectra of field-induced spin-density-wave (FISDW) states in quasi-one dimensional (Q1D) organic conductors, using an extended Su-Schrieffer-Heeger (SSH) model. We show that, in presence of half magnetic-flux FISDW state, the system exhibits topologically nontrivial phases, which can be characterized by a nonzero Chern number. The nontrivial evolution of the bulk bands with chemical potential in a topological phase transition is discussed. We show that the system can have a similar phase diagram which is discussed in the Haldane's model. We suggest that the topological feature should be tested experimentally in this organic system. These studies enrich the theoretical research on topologically nontrivial phases in the Q1D lattice system as compared to the Haldane topological phase appearing in the two-dimensional lattices. PMID:26612317

We explore topological phase transition, which involves the energy spectra of field-induced spin-density-wave (FISDW) states in quasi-one dimensional (Q1D) organic conductors, using an extended Su-Schrieffer-Heeger (SSH) model. We show that, in presence of half magnetic-flux FISDW state, the system exhibits topologically nontrivial phases, which can be characterized by a nonzero Chern number. The nontrivial evolution of the bulk bands with chemical potential in a topological phase transition is discussed. We show that the system can have a similar phase diagram which is discussed in the Haldane’s model. We suggest that the topological feature should be tested experimentally in this organic system. These studies enrich the theoretical research on topologically nontrivial phases in the Q1D lattice system as compared to the Haldane topological phase appearing in the two-dimensional lattices.

We study the effect of electron-phonon interactions in the band topology of Dirac insulators, both at zero and finite temperature. Elaborating on recent theoretical work, we determine how and when phonons can drive a trivial insulator into a topological insulating phase. As an application, we evaluate the temperature-dependence of the critical thickness for the topologicaltransition in CdTe/HgTe quantum wells.

The recently proposed Cohesive Homotopy Type Theory is exploited as a formal foundation for central concepts in Topological and Geometrical Quantum Computation. Specifically the Cohesive Homotopy Type Theory provides a formal, logical approach to concepts like smoothness, cohomology and Khovanov homology; and such approach permits to clarify the quantum algorithms in the context of Topological and Geometrical Quantum Computation. In particular we consider the so-called "open-closed stringy topological quantum computer" which is a theoretical topological quantum computer that employs a system of open-closed strings whose worldsheets are open-closed cobordisms. The open-closed stringy topological computer is able to compute the Khovanov homology for tangles and for hence it is a universal quantum computer given than any quantum computation is reduced to an instance of computation of the Khovanov homology for tangles. The universal algebra in this case is the Frobenius Algebra and the possible open-closed stringy topological quantum computers are forming a symmetric monoidal category which is equivalent to the category of knowledgeable Frobenius algebras. Then the mathematical design of an open-closed stringy topological quantum computer is involved with computations and theorem proving for generalized Frobenius algebras. Such computations and theorem proving can be performed automatically using the Automated Theorem Provers with the TPTP language and the SMT-solver Z3 with the SMT-LIB language. Some examples of application of ATPs and SMT-solvers in the mathematical setup of an open-closed stringy topological quantum computer will be provided.

Axion electrodynamics, first proposed in the context of particle physics, manifests itself in condensed matter physics in the topological field theory description of 3 d topological insulators and gives rise to magnetoelectric effect, where applying magnetic (electric) field B (E ) induces polarization (magnetization) p (m ) . We use linear response theory to study the associated topological current using the Fu-Kane-Mele model of 3 d topological insulators in the presence of time-dependent uniform weak magnetic field. By computing the dynamical current susceptibility χij jpjp(ω ) , we discover from its static limit an `order parameter' of the topological phase transition between weak topological (or ordinary) insulator and strong topological insulator, found to be continuous. The χij jpjp(ω ) shows a sign-changing singularity at a critical frequency with suppressed strength in the topological insulating state. Our results can be verified in current noise experiment on 3 d TI candidate materials for the detection of such topological phase transition.

The topological phases originating in spin-orbital coupling systems have attracted great attention in modern condensed matter physics. Many interesting phenomena have been found in recent theoretical and experimental works, such as the integer and fractional quantum Hall effect, topological band insulator, topological Mott insulator, and topological superconductor. We have investigated the topological phase transition on honeycomb lattice with third neighbor hooping by employing the cellular dynamical mean-field theory combining with the continuous-time Monte Carlo method. The non-trivial topological insulator can be found by observing the spin Chern number directly, and the effects of the third neighbor hopping and interaction are also discussed. Furthermore, we also provide the whole phase diagram for interaction, third neighbor hopping, and temperature. This work is supported by the Texas Center for Superconductivity at the University of Houston and by the Robert A. Welch Foundation under Grant No. E-1146.

The critical point of a topological phase transition is described by a conformal field theory. Finite-size corrections give rise to a scaling function away from criticality for both energy and entanglement entropy of the system. While in the past the scaling function for the usual von Neumann entropy was found to be equal for the trivial and the topological side of the transition, we find that the scaling functions for energy and Renyi entropy with α > 1 are different for the two sides. This provides an easy tool to distinguish between the trivial and topological phases near criticality.

We propose a simple approach to realize a topological phase transition using a spatial periodic potential. As an example, we examine the electronic structures of HgTe/CdTe quantum wells, and demonstrate that their band structures can be effectively manipulated by the periodic potential. At a critical potential, we find that a conventional band insulator undergoes a topological phase transition into a quantum spin Hall system, which is characterized by an abrupt change of the spin Chern number and emerging edge states. Our proposal provides an interesting way to dynamically turn on or off topologically protected edge states for application in switching devices.

We theoretically verify that the symmetry breaking in spherical resonators can result in a fractal frequency spectrum that is full of numerous new accidental degeneracies to cluster around the unperturbed degenerate cavity. We further experimentally discover that the fractal frequency spectrum excellently reflects the intimate connection between the emission power and the degenerate mode numbers. It is observed that the wave distributions of lasing modes at the accidental degeneracies are strongly concentrated on three-dimensional (3D) geometrictopology. Considering the overlapping effect, the wave representation of the coherent states is analytically derived to manifest the observed 3D geometric surfaces.

We propose a new way of using geometrictransitions to study metastable vacua in string theory and certain confining gauge theories. The gauge theories in question are N=2 supersymmetric theories deformed to N=1 by superpotential terms. We first geometrically engineer supersymmetry-breaking vacua by wrapping D5 branes on rigid 2-cycles in noncompact Calabi-Yau geometries, such that the central charges of the branes are misaligned. In a limit of slightly misaligned charges, this has a gauge theory description, where supersymmetry is broken by Fayet-Iliopoulos D-terms. Geometrictransitions relate these configurations to dual Calabi-Yaus with fluxes, where H_RR, H_NS and dJ are all nonvanishing. We argue that the dual geometry can be effectively used to study the resulting non-supersymmetric, confining vacua

We consider electron topologicaltransitions associated with certain points of band-contact lines in metals. These transitions are 31/2 kind according to the classification of Lifshits and are widespread in metals with inversion symmetry and a weak spin-orbit interaction. The 31/2 -order transitions can be detected with the magnetic susceptibility. As an example, we consider these transitions in graphite.

Topology, despite its mathematical abstractness, often manifests itself in physics and plays a pivotal role in our understanding of natural phenomena. Notable examples include the discoveries of topological phases in condensed matter systems which have changed the modern conception of phases of matter. The global nature of topological ordering, however, makes direct experimental probing an outstanding challenge. Present experimental tools are mainly indirect and inadequate for studying such properties at a fundamental level. Here, we employ the exquisite control afforded by superconducting quantum circuits to directly investigate topological properties of quantum spin systems. The essence of our approach is to infer local curvature by measuring the deflection of quantum trajectories topological properties are then revealed from a quantum analog of the Gauss-Bonnet theorem. We benchmark our technique by constructing the topological phase diagram of the celebrated Haldane model. The nature of the individual phases is revealed by visualizing their microscopic spin texture and evolution across the transition. Furthermore, we demonstrate the power of our method in studying the topology of interacting quantum systems, utilizing a novel qubit architecture which enables control over every term in a two-qubit Hamiltonian. We discovered an interaction-driven topological phase, whose emergence is understood by fully exploring the parameter-space of the Hamiltonian. Our work establishes a generalizable experimental platform to study fundamental aspects of topological phenomena in quantum systems. NSF Grants: DMR-0907039 and DMR-1029764.

We analyze the two-dimensional supersymmetric linear σ-model with U(1) gauge symmetries that includes a Calabi-Yau phase and a possible Landau-Ginzburg phase. We demonstrate the topology changing transitions among the generic vacua of various linear σ-models. In the supersymmetric transition the determinantal contraction naturally arises.

Despite the recent progress in physical control and manipulation of various condensed matter, atomic, and particle systems, including individual atoms and photons, our ability to control topological defects remains limited. Recently, controlled generation, spatial translation, and stretching of topological point and line defects have been achieved using laser tweezers and liquid crystals as model defect-hosting systems. However, many modes of manipulation remain hindered by limitations inherent to optical trapping. To overcome some of these limitations, we integrate holographic optical tweezers with a magnetic manipulation system, which enables fully holonomic manipulation of defects by means of optically and magnetically controllable colloids used as "handles" to transfer forces and torques to various liquid crystal defects. These colloidal handles are magnetically rotated around determined axes and are optically translated along three-dimensional pathways while mechanically attached to defects, which, combined with inducing spatially localized nematic-isotropic phase transitions, allow for geometrically unrestricted control of defects, including previously unrealized modes of noncontact manipulation, such as the twisting of disclination clusters. These manipulation capabilities may allow for probing topological constraints and the nature of defects in unprecedented ways, providing the foundation for a tabletop laboratory to expand our understanding of the role defects play in fields ranging from subatomic particle physics to early-universe cosmology.

Abstract One of the first proposals for a two-dimensional topological insulator was made for graphene, the so called Kane-Mele model, but the very low spin-orbit coupling makes this phase undetectable. It has been suggested that randomly depositing certain heavy adatoms can amplify the effect by many orders, and that a dilute concentration should be enough to open a detectable topological gap. Still lacking, however, is a precise determination of the critical density of random adatoms based in the evolution of the topological index. Based in a finite size analysis of the topological index as a function of the density of randomly distributed adatoms, and also on the localization properties of the system accessed through the Lyapunov exponent, we not only determine the critical density but also establish the nature of this peculiar topologicaltransition. EC acknowledge the financial support of FCT-Portugal through Grant No. EXPL/FIS-NAN/1720/2013.

In this talk I describe some recent work on unusual correlated phases that may be found in bulk transition metal oxides with strong spin-orbit coupling. I will focus on model Hamiltonian studies that are motivated by the pyrocholore iridates, though the correlated topological phases described may appear in a much broader class of materials. I will describe a variety of fractionalized topological phases protected by time-reversal and crystalline symmetries: The weak topological Mott insulator (WTMI), the TI* phase, and the topological crystalline Mott insulator (TCMI). If time permits, I will also discuss closely related heterostructures of pyrochlore iridates in a bilayer and trilayer film geometry. These quasi-two dimensional systems may exhibit a number of interesting topological and magnetic phases. This work is generously funded by the ARO, DARPA, and the NSF.

It is expected that the interplay between nontrivial band topology and strong electron correlation will lead to very rich physics. Thus a controlled study of the competition between topology and correlation is of great interest. Here, employing large-scale quantum Monte Carlo simulations, we provide a concrete example of the Kane-Mele-Hubbard model on an AA-stacking bilayer honeycomb lattice with interlayer antiferromagnetic interaction. Our simulation identified several different phases: a quantum spin Hall insulator (QSH), an x y -plane antiferromagnetic Mott insulator, and an interlayer dimer-singlet insulator. Most importantly, a bona fide topological phase transition between the QSH and the dimer-singlet insulators, purely driven by the interlayer antiferromagnetic interaction, is found. At the transition, the spin and charge gap of the system close while the single-particle excitations remain gapped, which means that this transition has no mean-field analog and it can be viewed as a transition between bosonic symmetry-protected topological (SPT) states. At one special point, this transition is described by a (2 +1 )d O (4 ) nonlinear sigma model with exact S O (4 ) symmetry and a topological term at exactly Θ =π . The relevance of this work towards more general interacting SPT states is discussed.

The search for Majorana fermions has been concentrated in topological insulators or superconductors. In general, the existence of these modes requires the presence of spin–orbit interactions and of an external magnetic field. The former implies in having systems with broken inversion symmetry, while the latter breaks time reversal invariance. In a recent paper, we have shown that a two-band metal with an attractive inter-band interaction has non-trivial superconducting properties, if the k-dependent hybridization is anti-symmetric in the wave-vector. This is the case, if the crystalline potential mixes states with different parities as for orbitals with angular momentum l and l+1. In this paper we take into account the effect of an external magnetic field, not considered in the previous investigation, in a two-band metal and show how it modifies the topological properties of its superconducting state. We also discuss the conditions for the appearance of Majorana fermions in this system.

Topologically ordered phase has emerged as one of most exciting concepts that not only broadens our understanding of phases of matter, but also has been found to have potential application in fault-tolerant quantum computation. The direct measurement of topological properties, however, is still a challenge, especially in interacting quantum system. Here we realize two to four spin one-dimensional Heisenberg chains using nuclear magnetic resonance simulators and observe interaction-induced topologicaltransitions, where Berry curvature in the parameter space of Hamiltonian is probed by means of dynamical response and then the first Chern number is extracted by integrating the curvature over the closed surface. The utilized experimental method provides a powerful means to explore topological phenomena in quantum systems with many-body interactions.

In this paper we study the quantum dynamics of a neutral particle in the presence of a topological defect. We investigate the appearance of a geometric phase in the relativistic quantum dynamics of a neutral particle which possesses permanent magnetic and electric dipole moments in the presence of an electromagnetic field in this curved space-time. The nonrelativistic quantum dynamics are investigated using the Foldy-Wouthuysen expansion. The gravitational Aharonov-Casher and He-McKellar-Wilkens effects are investigated for a series of electric and magnetic field configurations.

We used density functional theory to study the geometric and electronic structure of dimerized and one-dimensionally polymerized corannulene as ultra-narrow graphene ribbons with corrugation and topological defects. Our computations reveal that the relative stability and electronic structure of dimerized and polymerized corannulene are sensitive to the intermolecular covalent networks. The energy gap between the highest occupied and lowest unoccupied states of corannulene dimers is narrower than that of isolated corannulene. The corannulene polymers are semiconductors with a direct energy gap of about 1 eV depending on intermolecular bonds. The polymers possess moderate mechanical stiffness having Young's moduli of 200 GPa.

We investigate the quantum phase transition of an atomic ensemble trapped in a single-mode optical cavity via the geometric phase and quantum Fisher information of an extra probe atom which is injected into the optical cavity and interacts with the cavity field. We also find that the geometric quantum correlation between two probe atoms exhibits a double sudden transition phenomenon and show this double sudden transition phenomenon is closely associated with the quantum phase transition of the atomic ensemble. Furthermore, we propose a theoretical scheme to prolong the frozen time during which the geometric quantum correlation remains constant by applying time-dependent electromagnetic field.

We study the two-dimensional topological superconductors of spinless fermions in a checkerboard-lattice Chern-insulator model. With the short-range p-wave superconducting pairing, multifarious topological quantum phase transitions have been found and several phases with high Chern numbers have been observed. We have established a rich phase diagram for these topological superconducting states. A finite-size checkerboard-lattice cylinder with a harmonic trap potential has been further investigated. Based upon the self-consistent numerical calculations of the Bogoliubov-de Gennes equations, various phase transitions have also been identified at different regions of the system. Multiple pairs of Majorana fermions are found to be well-separated and localized at the phase boundaries between the phases characterized by different Chern numbers. PMID:27329219

We study the two-dimensional topological superconductors of spinless fermions in a checkerboard-lattice Chern-insulator model. With the short-range p-wave superconducting pairing, multifarious topological quantum phase transitions have been found and several phases with high Chern numbers have been observed. We have established a rich phase diagram for these topological superconducting states. A finite-size checkerboard-lattice cylinder with a harmonic trap potential has been further investigated. Based upon the self-consistent numerical calculations of the Bogoliubov-de Gennes equations, various phase transitions have also been identified at different regions of the system. Multiple pairs of Majorana fermions are found to be well-separated and localized at the phase boundaries between the phases characterized by different Chern numbers. PMID:27329219

Recent ab initio calculations and experiments reported insulating-semimetallic phase transitions in multilayer phosphorene under a perpendicular dc field, pressure, or doping, as a possible route to realize topological phases. In this work, we show that even a monolayer phosphorene may undergo Lifshitz transitions toward semimetallic and topological insulating phases, provided it is rapidly driven by in-plane time-periodic laser fields. Based on a four-orbital tight-binding description, we give an inversion-symmetry-based prescription in order to apprehend the topology of the photon-renormalized band structure, up to the second order in the high-frequency limit. Apart from the initial band insulating behavior, two additional phases are thus identified. A semimetallic phase with massless Dirac electrons may be induced by linear polarized fields, whereas elliptic polarized fields are likely to drive the material into an anomalous quantum Hall phase.

Recent experiments have produced mounting evidence of Majorana zero modes in nanowire-superconductor hybrids. Signatures of an expected topological phase transition accompanying the onset of these modes nevertheless remain elusive. We investigate a fundamental question concerning this issue: Do well-formed Majorana modes necessarily entail a sharp phase transition in these setups? Assuming reasonable parameters, we argue that finite-size effects can dramatically smooth this putative transition into a crossover, even in systems large enough to support well-localized Majorana modes. We propose overcoming such finite-size effects by examining the behavior of low-lying excited states through tunneling spectroscopy. In particular, the excited-state energies exhibit characteristic field and density dependence, and scaling with system size, that expose an approaching topological phase transition. We suggest several experiments for extracting the predicted behavior. As a useful byproduct, the protocols also allow one to measure the wire's spin-orbit coupling directly in its superconducting environment.

An analysis of known experimental literature data on the temperature dependence of magnetic susceptibility of beryllium. It is shown that this dependence can be explained if we take into account that beryllium has an electron topologicaltransition of 3½ kind near the Fermi level.

We find numerical and empirical evidence for dynamical, structural and topological phase transitions on the (German) Frankfurt Stock Exchange (FSE) in the temporal vicinity of the worldwide financial crash. Using the Minimal Spanning Tree (MST) technique, a particularly useful canonical tool of the graph theory, two transitions of the topology of a complex network representing the FSE were found. The first transition is from a hierarchical scale-free MST representing the stock market before the recent worldwide financial crash, to a superstar-like MST decorated by a scale-free hierarchy of trees representing the market’s state for the period containing the crash. Subsequently, a transition is observed from this transient, (meta)stable state of the crash to a hierarchical scale-free MST decorated by several star-like trees after the worldwide financial crash. The phase transitions observed are analogous to the ones we obtained earlier for the Warsaw Stock Exchange and more pronounced than those found by Onnela-Chakraborti-Kaski-Kertész for the S&P 500 index in the vicinity of Black Monday (October 19, 1987) and also in the vicinity of January 1, 1998. Our results provide an empirical foundation for the future theory of dynamical, structural and topological phase transitions on financial markets.

The spin-helical Dirac fermion topological surface states in a topological insulator nanowire or nanoribbon promise novel topological devices and exotic physics such as Majorana fermions. Here, we report local and non-local transport measurements in Bi2Te3 topological insulator nanoribbons that exhibit quasi-ballistic transport over ∼2 μm. The conductance versus axial magnetic flux Φ exhibits Aharonov-Bohm oscillations with maxima occurring alternately at half-integer or integer flux quanta (Φ0 = h/e, where h is Planck's constant and e is the electron charge) depending periodically on the gate-tuned Fermi wavevector (kF) with period 2π/C (where C is the nanoribbon circumference). The conductance versus gate voltage also exhibits kF-periodic oscillations, anti-correlated between Φ = 0 and Φ0/2. These oscillations enable us to probe the Bi2Te3 band structure, and are consistent with the circumferentially quantized topological surface states forming a series of one-dimensional subbands, which undergo periodic magnetic field-induced topologicaltransitions with the disappearance/appearance of the gapless Dirac point with a one-dimensional spin helical mode. PMID:26780658

The spin-helical Dirac fermion topological surface states in a topological insulator nanowire or nanoribbon promise novel topological devices and exotic physics such as Majorana fermions. Here, we report local and non-local transport measurements in Bi2Te3 topological insulator nanoribbons that exhibit quasi-ballistic transport over ∼2 μm. The conductance versus axial magnetic flux Φ exhibits Aharonov–Bohm oscillations with maxima occurring alternately at half-integer or integer flux quanta (Φ0 = h/e, where h is Planck's constant and e is the electron charge) depending periodically on the gate-tuned Fermi wavevector (kF) with period 2π/C (where C is the nanoribbon circumference). The conductance versus gate voltage also exhibits kF-periodic oscillations, anti-correlated between Φ = 0 and Φ0/2. These oscillations enable us to probe the Bi2Te3 band structure, and are consistent with the circumferentially quantized topological surface states forming a series of one-dimensional subbands, which undergo periodic magnetic field-induced topologicaltransitions with the disappearance/appearance of the gapless Dirac point with a one-dimensional spin helical mode.

In this study, we examine effective field theories of superconducting phases with topological order, making a connection to proposed realizations of exotic topological phases (including those hosting Ising and Fibonacci anyons) in superconductor-quantum Hall heterostructures. Our effective field theories for the non-Abelian superconducting states are non-Abelian Chern-Simons theories in which the condensation of vortices carrying non-Abelian gauge flux leads to the associated Abelian quantum Hall states. This Chern-Simons-Higgs condensation process is dual to the emergence of superconducting non-Abelian topological phases in coupled chain constructions. In such transitions, the chiral central charge of the system generally changes, so they fall outside the description of bosonic condensation transitions put forth by Bais and Slingerland [F. A. Bais and J. K. Slingerland, Phys. Rev. B 79, 045316 (2009), 10.1103/PhysRevB.79.045316] (though the two approaches agree when the described transitions coincide). Our condensation process may be generalized to Chern-Simons theories based on arbitrary Lie groups, always describing a transition from a Lie algebra to its Cartan subalgebra. We include several instructive examples of such transitions.

We study the effects of topological (connectivity) disorder on phase transitions. We identify a broad class of random lattices whose disorder fluctuations decay much faster with increasing length scale than those of generic random systems, yielding a wandering exponent of ω=(d-1)/(2d) in d dimensions. The stability of clean critical points is thus governed by the criterion (d+1)ν>2 rather than the usual Harris criterion dν>2, making topological disorder less relevant than generic randomness. The Imry-Ma criterion is also modified, allowing first-order transitions to survive in all dimensions d>1. These results explain a host of puzzling violations of the original criteria for equilibrium and nonequilibrium phase transitions on random lattices. We discuss applications, and we illustrate our theory by computer simulations of random Voronoi and other lattices. PMID:25279615

In a one-dimensional spinless p-wave superconductor with coherence length ξ, disorder induces a phase transition between a topologically nontrivial phase and a trivial insulating phase at the critical mean-free path l=ξ/2. Here, we show that a multichannel spinless p-wave superconductor goes through an alternation of topologically trivial and nontrivial phases upon increasing the disorder strength, the number of phase transitions being equal to the channel number N. The last phase transition, from a nontrivial phase into the trivial phase, takes place at a mean-free path l=ξ/(N+1), parametrically smaller than the critical mean-free path in one dimension. Our result is valid in the limit that the wire width W is much smaller than the superconducting coherence length ξ.

The guidance of human sperm cells under confinement in quasi-2D microchambers is investigated using a purely physical method to control their distribution. Transport property measurements and simulations are performed with diluted sperm populations, for which effects of geometrical guidance and concentration are studied in detail. In particular, a trapping transition at convex angular wall features is identified and analyzed. We also show that highly efficient microratchets can be fabricated by using curved asymmetric obstacles to take advantage of the spermatozoa specific swimming strategy.

Spin orbit coupled semiconductor nanowires in proximity to ordinary S wave superconductor exhibit a topological phase which supports Majorana fermions at the two ends of the nanowire. A signature of Majorana fermions would be a zero bias conductance peak. Indeed such a peak has been observed in recent experiments but at the same time alternate non topological mechanisms have been suggested to explain appearance of the zero bias peak. Here we demonstrate that the zero bias conductance peak from Majorana fermions must appear in a correlated way between the two ends. We analyze how this peculiarity can be used as a signature of the topological phase transition linked to the appearance of Majorana modes and thus can be used to experimentally distinguish between competing theoretical mechanisms. We acknowledge support from Physics Frontier Center and Maryland Startup Fund.

We introduce and theoretically demonstrate a quantum metamaterial made of dense ultracold neutral atoms loaded into an inherently defect-free artificial crystal of light, immune to well-known critical challenges inevitable in conventional solid-state platforms. We demonstrate an all-optical control, on ultrafast time scales, over the photonic topologicaltransition of the isofrequency contour from an open to closed topology at the same frequency. This atomic lattice quantum metamaterial enables a dynamic manipulation of the decay rate branching ratio of a probe quantum emitter by more than an order of magnitude. Our proposal may lead to practically lossless, tunable, and topologically reconfigurable quantum metamaterials, for single or few-photon-level applications as varied as quantum sensing, quantum information processing, and quantum simulations using metamaterials.

We introduce and theoretically demonstrate a quantum metamaterial made of dense ultracold neutral atoms loaded into an inherently defect-free artificial crystal of light, immune to well-known critical challenges inevitable in conventional solid-state platforms. We demonstrate an all-optical control, on ultrafast time scales, over the photonic topologicaltransition of the isofrequency contour from an open to closed topology at the same frequency. This atomic lattice quantum metamaterial enables a dynamic manipulation of the decay rate branching ratio of a probe quantum emitter by more than an order of magnitude. Our proposal may lead to practically lossless, tunable, and topologically reconfigurable quantum metamaterials, for single or few-photon-level applications as varied as quantum sensing, quantum information processing, and quantum simulations using metamaterials. PMID:27152810

Topologicaltransition of dispersion in anisotropic metamaterials, in which isofrequency contour changes from a closed ellipsoid to an open hyperboloid, is usually realized by changing the sign of one component of permittivity (ɛ) or permeability (μ) from positive to negative. However, we show that topologicaltransition of dispersion can occur by tuning the imaginary part of ɛ(μ) while fixing the real part of ɛ(μ). By adding different lumped resistors into two-dimensional transmission-line-based metamaterials, we just tune the imaginary part of μ at a fixed frequency. With the increase of loss, we measure the different emission patterns from a point source in the metamaterials to observe the changing process of isofrequency contours.

Ab-initio molecular dynamics, supported by inelastic neutron scattering and nuclear resonant inelastic x-ray scattering, showed an anomalous thermal softening of the M5- phonon mode in B2-ordered FeTi that could not be explained by phonon-phonon interactions or electron-phonon interactions calculated at low temperatures. A computational investigation showed that the Fermi surface undergoes a novel thermally-driven electronic topologicaltransition, in which new features of the Fermi surface arise at elevated temperatures. The thermally-induced electronic topologicaltransition causes an increased electronic screening for the atom displacements in the M5- phonon mode, and an adiabatic electron-phonon interaction with an unusual temperature dependence.

Ab initio molecular dynamics, supported by inelastic neutron scattering and nuclear resonant inelastic x-ray scattering, showed an anomalous thermal softening of the M_{5}^{-} phonon mode in B2-ordered FeTi that could not be explained by phonon-phonon interactions or electron-phonon interactions calculated at low temperatures. A computational investigation showed that the Fermi surface undergoes a novel thermally driven electronic topologicaltransition, in which new features of the Fermi surface arise at elevated temperatures. The thermally induced electronic topologicaltransition causes an increased electronic screening for the atom displacements in the M_{5}^{-} phonon mode and an adiabatic electron-phonon interaction with an unusual temperature dependence. PMID:27563978

Ab initio molecular dynamics, supported by inelastic neutron scattering and nuclear resonant inelastic x-ray scattering, showed an anomalous thermal softening of the M5- phonon mode in B 2 -ordered FeTi that could not be explained by phonon-phonon interactions or electron-phonon interactions calculated at low temperatures. A computational investigation showed that the Fermi surface undergoes a novel thermally driven electronic topologicaltransition, in which new features of the Fermi surface arise at elevated temperatures. The thermally induced electronic topologicaltransition causes an increased electronic screening for the atom displacements in the M5- phonon mode and an adiabatic electron-phonon interaction with an unusual temperature dependence.

In this paper, ab initio molecular dynamics, supported by inelastic neutron scattering and nuclear resonant inelastic x-ray scattering, showed an anomalous thermal softening of the M5- phonon mode in B2-ordered FeTi that could not be explained by phonon-phonon interactions or electron-phonon interactions calculated at low temperatures. A computational investigation showed that the Fermi surface undergoes a novel thermally driven electronic topologicaltransition, in which new features of the Fermi surface arise at elevated temperatures. Finally, the thermally induced electronic topologicaltransition causes an increased electronic screening for the atom displacements in the M5- phonon mode and an adiabatic electron-phonon interactionmore » with an unusual temperature dependence.« less

We use laser-cooled ion Coulomb crystals in the well-controlled environment of a harmonic radiofrequency ion trap to investigate phase transitions and defect formation. Topological defects in ion Coulomb crystals (kinks) have been recently proposed for studies of nonlinear physics with solitons and as carriers of quantum information. Defects form when a symmetry breaking phase transition is crossed non-adiabatically. For a second order phase transition, the Kibble-Zurek mechanism predicts that the formation of these defects follows a power law scaling in the rate of the transition. We demonstrate a scaling of defect density and describe kink dynamics and stability. We further discuss the implementation of mass defects and electric fields as first steps toward controlled kink preparation and manipulation.

Fathoming interplay between symmetry and topology of many-electron wave-functions deepens our understanding in quantum nature of many particle systems. Topology often protects zero-energy excitation, and in a certain class, symmetry is intrinsically tied to the topological protection. Namely, unless symmetry is broken, topological nature is intact. We study one specific case of such class, symmetry-protected line-nodal superconductors in three spatial dimensions (3d). Mismatch between phase spaces of order parameter fluctuation and line-nodal fermion excitation induces an exotic universality class in a drastic contrast to one of the conventional ϕ4 theory in 3d. Hyper-scaling violation and relativistic dynamic scaling with unusually large quantum critical region are main characteristics, and their implication in experiments is discussed. For example, continuous phase transition out of line-nodal superconductors has a linear phase boundary in a temperature-tuning parameter phase-diagram. This work was supported by the Brain Korea 21 PLUS Project of Korea Government and KAIST start-up funding.

We have studied a flocking model with binary interactions (binary flock), where the velocity of an agent depends on the velocity of only another agent and its own velocity, topped by the angular noise. The other agent is selected as the nth topological neighbor; the specific value of n being a fixed parameter of the problem. On the basis of extensive numerical simulation results, we argue that for n = 1, the phase transition from the ordered to the disordered phase of the flock is a special kind of discontinuous transition. Here, the order parameter does not flip-flop between multiple metastable states. It continues its initial disordered state for a period t(c), then switches over to the ordered state and remains in this state ever after. For n = 2, it is the usual discontinuous transition between two metastable states. Beyond this range, the continuous transitions are observed for n≥3. Such a system of binary flocks has been further studied using the hydrodynamic equations of motion. Linear stability analysis of the homogeneous polarized state shows that such a state is unstable close to the critical point and above some critical speed, which increases as we increase n. The critical noise strengths, which depend on the average correlation between a pair of topological neighbors, are estimated for five different values of n, which match well with their simulated values. PMID:26764659

Topological quantum phase transitions intrinsically intertwine self-similarity and topology of many-electron wave-functions, and divining them is one of the most significant ways to advance understanding in condensed matter physics. Our focus is to investigate an unconventional class of the transitions between insulators and Dirac semimetals whose description is beyond conventional pseudo relativistic Dirac Hamiltonian. At the transition without the long-range Coulomb interaction, the electronic energy dispersion along one direction behaves like a relativistic particle, linear in momentum, but along the other direction it behaves like a non-relativistic particle, quadratic in momentum. Various physical systems ranging from TiO2-VO2 heterostructure to organic material α-(BEDT-TTF)2I3 under pressure have been proposed to have such anisotropic dispersion relation. Here, we discover a novel quantum criticality at the phase transition by incorporating the long range Coulomb interaction. Unique interplay between the Coulomb interaction and electronic critical modes enforces not only the anisotropic renormalization of the Coulomb interaction but also marginally modified electronic excitation. In connection with experiments, we investigate several striking effects in physical observables of our novel criticality.

We have studied a flocking model with binary interactions (binary flock), where the velocity of an agent depends on the velocity of only another agent and its own velocity, topped by the angular noise. The other agent is selected as the n th topological neighbor; the specific value of n being a fixed parameter of the problem. On the basis of extensive numerical simulation results, we argue that for n = 1, the phase transition from the ordered to the disordered phase of the flock is a special kind of discontinuous transition. Here, the order parameter does not flip-flop between multiple metastable states. It continues its initial disordered state for a period tc, then switches over to the ordered state and remains in this state ever after. For n = 2, it is the usual discontinuous transition between two metastable states. Beyond this range, the continuous transitions are observed for n ≥3 . Such a system of binary flocks has been further studied using the hydrodynamic equations of motion. Linear stability analysis of the homogeneous polarized state shows that such a state is unstable close to the critical point and above some critical speed, which increases as we increase n . The critical noise strengths, which depend on the average correlation between a pair of topological neighbors, are estimated for five different values of n , which match well with their simulated values.

Topological quantum phase transitions intrinsically intertwine self-similarity and topology of many-electron wave-functions, and divining them is one of the most significant ways to advance understanding in condensed matter physics. Our focus is to investigate an unconventional class of the transitions between insulators and Dirac semimetals whose description is beyond conventional pseudo relativistic Dirac Hamiltonian. At the transition without the long-range Coulomb interaction, the electronic energy dispersion along one direction behaves like a relativistic particle, linear in momentum, but along the other direction it behaves like a non-relativistic particle, quadratic in momentum. Various physical systems ranging from TiO2-VO2 heterostructure to organic material α-(BEDT-TTF)2I3 under pressure have been proposed to have such anisotropic dispersion relation. Here, we discover a novel quantum criticality at the phase transition by incorporating the long range Coulomb interaction. Unique interplay between the Coulomb interaction and electronic critical modes enforces not only the anisotropic renormalization of the Coulomb interaction but also marginally modified electronic excitation. In connection with experiments, we investigate several striking effects in physical observables of our novel criticality. PMID:26791803

The honeycomb lattice of graphene is characterized by linear dispersion and pseudospin chirality of fermions on the Dirac cones. If lattice anisotropy is introduced, the Dirac cones stay intact but move in reciprocal space. Dirac point movement can lead to a topologicaltransition from semimetal to semiconductor when two inequivalent Dirac points merge, an idea that has attracted significant research interest. However, such movement normally requires unrealistically high lattice anisotropy. Here we show that anisotropic defects can break the C3 symmetry of graphene, leading to Dirac point drift in the Brillouin zone. Additionally, the long-range order in periodically patterned graphene can induce intervalley scattering between two inequivalent Dirac points, resulting in a semimetal-to-insulator topological phase transition. The magnitude and direction of Dirac point drift are predicted analytically, which are consistent with our first-principles electronic structure calculations. Thus, periodically patterned graphene can be used to study the fascinating physics associated with Dirac point movement and the corresponding phase transition.The honeycomb lattice of graphene is characterized by linear dispersion and pseudospin chirality of fermions on the Dirac cones. If lattice anisotropy is introduced, the Dirac cones stay intact but move in reciprocal space. Dirac point movement can lead to a topologicaltransition from semimetal to semiconductor when two inequivalent Dirac points merge, an idea that has attracted significant research interest. However, such movement normally requires unrealistically high lattice anisotropy. Here we show that anisotropic defects can break the C3 symmetry of graphene, leading to Dirac point drift in the Brillouin zone. Additionally, the long-range order in periodically patterned graphene can induce intervalley scattering between two inequivalent Dirac points, resulting in a semimetal-to-insulator topological phase transition. The

The magnetoresistance of layered organic conductors with a multisheet Fermi surface (FS) is studied theoretically under conditions of the Lifshitz topologicaltransition, where the FS topology may change in response to external effects acting on the conductor, such as pressure or doping with impurity atoms. Using as an example the Fermi surface consisting of a cylinder and two planes, which are slightly corrugated along the projection of the momentum pz=p n along the normal to the layers n, we analyze the magnetic-field dependence of the resistance and the Hall field in a strong external magnetic field H, where the cyclotron frequency ωc of the conduction electrons is much higher than their collision frequency 1/τ. In the immediate vicinity of the topologicaltransition, where the distance between the different sheets of the FS becomes small, an electron can move from one sheet of the FS to another with the probability w due to the magnetic breakdown. In this case, a quadratic increase of the electric resistance across the layers with magnetic field, which occurs in the absence of the magnetic breakdown, is replaced by a linear dependence on H for w ≥γ=1 /ωcτ , and then reaches saturation for (1 -w )≤γ . The Hall field depends substantially on the probability of a magnetic breakdown, but in the case of ωcτ≫1 , its asymptote is independent of τ for all values of w. At w = 1, the quasi-planar sheets of the Fermi surface touch the corrugated cylinders, and under further perturbation acting on the conductor, there occurs a break of a flat sheet along the line of contact. As a result, separate sections of the flat FS sheet together with the cut halves of the corrugated cylinder form a new corrugated cylinder with the sign of charge carriers reversed. This is not the only scenario of the Lifshitz topologicaltransition. Studies of the Hall effect will allow us to obtain further important information on the nature of changes in the topological structure of

We predict a quantum phase transition in fcc Ca under hydrostatic pressure. Using density functional theory, we find, at pressures below 80 kbar, the topology of the electron charge density is characterized by nearest neighbor atoms connected through bifurcated bond paths and deep minima in the octahedral holes. At pressures above 80 kbar, the atoms bond through non-nuclear maxima that form in the octahedral holes. This topological change in the charge density softens the C' elastic modulus of fcc Ca, while C44 remains unchanged. We propose an order parameter based on applying Morse theory to the charge density, and we show that near the critical point it follows the expected mean-field scaling law with reduced pressure. PMID:21231679

We predict a quantum phase transition in fcc Ca under hydrostatic pressure. Using density functional theory, we find, at pressures below 80 kbar, the topology of the electron charge density is characterized by nearest neighbor atoms connected through bifurcated bond paths and deep minima in the octahedral holes. At pressures above 80 kbar, the atoms bond through non-nuclear maxima that form in the octahedral holes. This topological change in the charge density softens the C' elastic modulus of fcc Ca, while C44 remains unchanged. We propose an order parameter based on applying Morse theory to the charge density, and we show that near the critical point it follows the expected mean-field scaling law with reduced pressure.

Curvature and mechanics are intimately connected for thin materials, and this coupling between geometry and physical properties is readily seen in folded structures from intestinal villi and pollen grains to wrinkled membranes and programmable metamaterials. While the well-known rules and mechanisms behind folding a flat surface have been used to create deployable structures and shape transformable materials, folding of curved shells is still not fundamentally understood. Shells naturally deform by simultaneously bending and stretching, and while this coupling gives them great stability for engineering applications, it makes folding a surface of arbitrary curvature a nontrivial task. Here we discuss the geometry of folding a creased shell, and demonstrate theoretically the conditions under which it may fold smoothly. When these conditions are violated we show, using experiments and simulations, that shells undergo rapid snapping motion to fold from one stable configuration to another. Although material asymmetry is a proven mechanism for creating this bifurcation of stability, for the case of a creased shell, the inherent geometry itself serves as a barrier to folding. We discuss here how two fundamental geometric concepts, creases and curvature, combine to allow rapid transitions from one stable state to another. Independent of material system and length scale, the design rule that we introduce here explains how to generate snapping transitions in arbitrary surfaces, thus facilitating the creation of programmable multistable materials with fast actuation capabilities. PMID:26294253

In the course of a non-equilibrium continuous phase transition, the dynamics ceases to be adiabatic in the vicinity of the critical point as a result of the critical slowing down (the divergence of the relaxation time in the neighborhood of the critical point). This enforces a local choice of the broken symmetry and can lead to the formation of topological defects. The Kibble-Zurek mechanism (KZM) was developed to describe the associated nonequilibrium dynamics and to estimate the density of defects as a function of the quench rate through the transition. During recent years, several new experiments investigating formation of defects in phase transitions induced by a quench both in classical and quantum mechanical systems were carried out. At the same time, some established results were called into question. We review and analyze the Kibble-Zurek mechanism focusing in particular on this surge of activity, and suggest possible directions for further progress.

Crystal-structure topologies, represented by periodic nets, are described by labelled quotient graphs (or voltage graphs). Because the edge space of a finite graph is the direct sum of its cycle and co-cycle spaces, a Euclidian representation of the derived periodic net is provided by mapping a basis of the cycle and co-cycle spaces to a set of real vectors. The mapping is consistent if every cycle of the basis is mapped on its own net voltage. The sum of all outgoing edges at every vertex may be chosen as a generating set of the co-cycle space. The embedding maps the cycle space onto the lattice L. By analogy, the concept of the co-lattice L* is defined as the image of the generators of the co-cycle space; a co-lattice vector is proportional to the distance vector between an atom and the centre of gravity of its neighbours. The pair (L, L*) forms a complete geometric descriptor of the embedding, generalizing the concept of barycentric embedding. An algebraic expression permits the direct calculation of fractional coordinates. Non-zero co-lattice vectors allow nets with collisions, displacive transitions etc. to be dealt with. The method applies to nets of any periodicity and dimension, be they crystallographic nets or not. Examples are analyzed: α-cristobalite, the seven unstable 3-periodic minimal nets etc. PMID:21173475

We study the effects of topological (connectivity) disorder on phase transitions. We identify a broad class of random lattices whose disorder fluctuations decay much faster with increasing length scale than those of generic random systems, yielding a wandering exponent of ω = (d - 1) / (2 d) in d dimensions. The stability of clean critical points is thus governed by the criterion (d + 1) ν > 2 rather than the usual Harris criterion dν > 2 , making topological disorder less relevant than generic randomness. The Imry-Ma criterion is also modified, allowing first-order transitions to survive in all dimensions d > 1 . These results explain a host of puzzling violations of the original criteria for equilibrium and nonequilibrium phase transitions on random lattices. We discuss applications, and we illustrate our theory by computer simulations of random Voronoi and other lattices. This work was supported by the NSF under Grant Nos. DMR-1205803 and PHYS-1066293. We acknowledge the hospitality of the Aspen Center for Physics.

Many physical systems can be modeled as large sets of domains "glued" together along boundaries—biological cells meet along cell membranes, soap bubbles meet along thin films, countries meet along geopolitical boundaries, and metallic crystals meet along grain interfaces. Each class of microstructures results from a complex interplay of initial conditions and particular evolutionary dynamics. The statistical steady-state microstructure resulting from isotropic grain growth of a polycrystalline material is canonical in that it is the simplest example of a cellular microstructure resulting from a gradient flow of an energy that is directly proportional to the total length or area of all cell boundaries. As many properties of polycrystalline materials depend on their underlying microstructure, a more complete understanding of the grain growth steady state can provide insight into the physics of a broad range of everyday materials. In this paper we report geometric and topological features of these canonical two- and three-dimensional steady-state microstructures obtained through extensive simulations of isotropic grain growth.

Many physical systems can be modeled as large sets of domains "glued" together along boundaries-biological cells meet along cell membranes, soap bubbles meet along thin films, countries meet along geopolitical boundaries, and metallic crystals meet along grain interfaces. Each class of microstructures results from a complex interplay of initial conditions and particular evolutionary dynamics. The statistical steady-state microstructure resulting from isotropic grain growth of a polycrystalline material is canonical in that it is the simplest example of a cellular microstructure resulting from a gradient flow of an energy that is directly proportional to the total length or area of all cell boundaries. As many properties of polycrystalline materials depend on their underlying microstructure, a more complete understanding of the grain growth steady state can provide insight into the physics of a broad range of everyday materials. In this paper we report geometric and topological features of these canonical two- and three-dimensional steady-state microstructures obtained through extensive simulations of isotropic grain growth. PMID:26764854

The Hall response provides an important characterization of strongly correlated phases of matter. We study the Hall conductivity of interacting bosons on a lattice subjected to a magnetic field. We show that for any density or interaction strength, the Hall conductivity is characterized by an integer. We find that the phase diagram is intersected by topologicaltransitions between different values of this integer. These transitions lead to surprising effects, including sign reversal of the Hall conductivity and extensive regions in the phase diagram where it acquires a negative sign, which implies that flux flow is reversed in these regions—vortices there flow upstream. Our findings have immediate applications to a wide range of phenomena in condensed matter physics, which are effectively described in terms of lattice bosons. PMID:22109548

We demonstrate that the gauged BPS baby Skyrme model with a double vacuum potential allows for phase transitions from a non-solitonic to a solitonic phase, where the latter corresponds to a ferromagnetic liquid. Such a transition can be generated by increasing the external pressure P or by turning on an external magnetic field H. As a consequence, the topological phase where gauged BPS baby skyrmions exist, is a higher density phase. For smaller densities, obtained for smaller values of P and H, a phase without solitons is reached. We find the critical line in the P, H parameter space. Furthermore, in the soliton phase, we find the equation of state for the baby skyrmion matter V = V( P,H) at zero temperature, where V is the "volume", i.e., area of the solitons.

Virtual 3D city models are integrated complex compositions of spatial data of different themes, origin, quality, scale, and dimensions. Within this paper, we address the problem of spatial compatibility of geodata aiming to provide support for ad-hoc integration of virtual 3D city models including geodata of different sources and themes like buildings, terrain, and city furniture. In contrast to related work which is dealing with the integration of redundant geodata structured according to different data models and ontologies, we focus on the integration of complex 3D models of the same representation (here: CityGML) but regarding to the geometric-topological consistent matching of non-homologous objects, e.g. a building is connected to a road, and their geometric homogenisation. Therefore, we present an approach including a data model for a Geodata Join and the general concept of an integration procedure using the join information. The Geodata Join aims to bridge the lack of information between fragmented geodata by describing the relationship between adjacent objects from different datasets. The join information includes the geometrical representation of those parts of an object, which have a specific/known topological or geometrical relationship to another object. This part is referred to as a Connector and is either described by points, lines, or surfaces of the existing object geometry or by additional join geometry. In addition, the join information includes the specification of the connected object in the other dataset and the description of the topological and geometrical relationship between both objects, which is used to aid the matching process. Furthermore, the Geodata Join contains object-related information like accuracy values and restrictions of movement and deformation which are used to optimize the integration process. Based on these parameters, a functional model including a matching algorithm, transformation methods, and conditioned adjustment

and 2) topology-based methodologies to interactively visualize multidimensional data and extract risk-informed insights. Regarding item 1) we employ learning algorithms that aim to infer/predict simulation outcome and decide the coordinate in the input space of the next sample that maximize the amount of information that can be gained from it. Such methodologies can be used to both explore and exploit the input space. The later one is especially used for safety analysis scopes to focus samples along the limit surface, i.e. the boundaries in the input space between system failure and system success. Regarding item 2) we present a software tool that is designed to analyze multi-dimensional data. We model a large-scale nuclear simulation dataset as a high-dimensional scalar function defined over a discrete sample of the domain. First, we provide structural analysis of such a function at multiple scales and provide insight into the relationship between the input parameters and the output. Second, we enable exploratory analysis for users, where we help the users to differentiate features from noise through multi-scale analysis on an interactive platform, based on domain knowledge and data characterization. Our analysis is performed by exploiting the topological and geometric properties of the domain, building statistical models based on its topological segmentations and providing interactive visual interfaces to facilitate such explorations.

It was argued, and fought through numerical work that the results of non-dynamical Monte Carlo computer simulations cannot be applied to describe the formation of topological defects when the correlation length at the Ginzburg temperature is significantly smaller than the horizon size. To test the current hypothesis that infinite strings at formation are essentially described by Brownian walks of size the correlation length at the Ginzburg temperature, fields at the Ginzburg temperature were equilibrated. Infinite structure do not exist in equilibrium for reasonable definitions of the Ginzburg temperature, and horizons must be included in a proper treatment. A phase transition, from small-scale to large-scale string or domain wall structure, is found to occur very close to the Ginzburg temperature, in agreement with recent work. The formation process of domain walls and global strings were investigated through the breaking of initially ordered states. To mimic conditions in the early Universe, cooling times are chosen so that horizons exist in the sample volume when topological structure formation occurs. The classical fields are evolved in real-time by the numerical solution of Langevin equations of motion on a three dimensional spatial lattice. The results indicate that it is possible for most of the string energy to be in small loops, rather than in long strings, at formation.

Current assessment of cartilage is primarily based on identification of indirect markers such as joint space narrowing and increased subchondral bone density on x-ray images. In this context, phase contrast CT imaging (PCI-CT) has recently emerged as a novel imaging technique that allows a direct examination of chondrocyte patterns and their correlation to osteoarthritis through visualization of cartilage soft tissue. This study investigates the use of topological and geometrical approaches for characterizing chondrocyte patterns in the radial zone of the knee cartilage matrix in the presence and absence of osteoarthritic damage. For this purpose, topological features derived from Minkowski Functionals and geometric features derived from the Scaling Index Method (SIM) were extracted from 842 regions of interest (ROI) annotated on PCI-CT images of healthy and osteoarthritic specimens of human patellar cartilage. The extracted features were then used in a machine learning task involving support vector regression to classify ROIs as healthy or osteoarthritic. Classification performance was evaluated using the area under the receiver operating characteristic (ROC) curve (AUC). The best classification performance was observed with high-dimensional geometrical feature vectors derived from SIM (0.95 ± 0.06) which outperformed all Minkowski Functionals (p < 0.001). These results suggest that such quantitative analysis of chondrocyte patterns in human patellar cartilage matrix involving SIM-derived geometrical features can distinguish between healthy and osteoarthritic tissue with high accuracy.

We examine the zero-temperature phase diagram of the two-dimensional Levin-Wen string-net model with Fibonacci anyons in the presence of competing interactions. Combining high-order series expansions around three exactly solvable points and exact diagonalizations, we find that the non-Abelian doubled Fibonacci topological phase is separated from two nontopological phases by different second-order quantum critical points, the positions of which are computed accurately. These trivial phases are separated by a first-order transition occurring at a fourth exactly solvable point where the ground-state manifold is infinitely many degenerate. The evaluation of critical exponents suggests unusual universality classes. PMID:25167030

In this paper, we investigate analytically the properties of the disordered Bernoulli model of planar matching. This model is characterized by a topological phase transition, yielding complete planar matching solutions only above a critical density threshold. We develop a combinatorial procedure of arcs expansion that explicitly takes into account the contribution of short arcs and allows us to obtain an accurate analytical estimation of the critical value by reducing the global constrained problem to a set of local ones. As an application to a toy representation of the RNA secondary structures, we suggest generalized models that incorporate a one-to-one correspondence between the contact matrix and the RNA-type sequence, thus giving sense to the notion of effective non-integer alphabets.

The almost completely immiscible PbTe/CdTe heterostructure has recently become a prototype system for self-organized quantum dot formation based on solid-state phase separation. Here, we study by real-time transmission electron microscopy the topological transformations of two-dimensional PbTe-epilayers into, first, a quasi-one-dimensional percolation network and subsequently into zero-dimensional quantum dots. Finally, the dot size distribution coarsens by Ostwald ripening. The whole transformation sequence occurs during all stages in the fully coherent solid state by bulk diffusion. A model based on the numerical solution of the Cahn-Hilliard equation reproduces all relevant morphological and dynamic aspects of the experiments, demonstrating that this standard continuum approach applies to coherent solids down to nanometer dimensions. As the Cahn-Hilliard equation does not depend on atomistic details, the observed morphological transformations are general features of the model. To confirm the topological nature of the observed shape transitions, we developed a parameter-free geometric model. This, together with the Cahn-Hilliard approach, is in qualitative agreement with the experiments.

The coupling of a conventional s-wave superconductors to semiconductors with strong spin-orbit (SO) coupling, like e. g. InAs or InSb nanowires (NWs), gives rise to unconventional p-wave superconductivity that may become a topological superconductor (TS), which is a natural host for exotic edge modes with Majorana character. Recently the enhancement of the critical supercurrent Ic in a strong SO semiconducting Josephson junction (JJ) have been proposed as a new evidence of the sought-after Majorana bound states. Here we report on the first observation of the colossal Ic enhancement induced by an external magnetic field on a mesoscopic JJ formed by InAs NWs and Ti/Al leads. This anomalous enhancement appears precisely above a threshold magnetic field Bth orthogonal to the substrate and in junctions of different lengths, suggesting that the origin of the enhancement is intrinsic, i.e. it is not related to geometrical resonances in the junction. None of the standard phenomenon known in JJ, including e. g. Fraunhofer patterns or π-junction behavior, can explain this colossal enhancement while a topologicaltransition at Bth is qualitatively compatible with the observed phenomenology.

Electrically controlled band gap and topological electronic states are important for the next-generation topological quantum devices. In this letter, we study the electric field control of band gap and topological phase transitions in multilayer germanane. We find that although the monolayer and multilayer germananes are normal insulators, a vertical electric field can significantly reduce the band gap of multilayer germananes owing to the giant Stark effect. The decrease of band gap eventually leads to band inversion, transforming them into topological insulators with nontrivial Z2 invariant. The electrically controlled topological phase transition in multilayer germananes provides a potential route to manipulate topologically protected edge states and design topological quantum devices. This strategy should be generally applicable to a broad range of materials, including other two-dimensional materials and ultrathin films with controlled growth.

This paper uses (linearized) Kalman filters to estimate first-order geometric parameters (i.e., orientation of contact normals and location of contact points) that occur in force-controlled compliant motions. The time variance of these parameters is also estimated. In addition, transitions between contact situations can be monitored. The contact between the manipulated object and its environment is general, i.e., multiple contacts can occur at the same time, and both the topology and the geometry of each single contact are arbitrary. The two major theoretical contributions are (1) the integration of the general contact model, developed previously by the authors, into a state-space form suitable for recursive processing; and (2) the use of the reciprocity constraint between ideal contact forces and motion freedoms as the measurement equation of the Kalman filter. The theory is illustrated by full 3-D experiments. The approach of this paper allows a breakthrough in the state of the art dominated by the classical, orthogonal contact models of Mason that can only cope with a limited (albeit important) subset of all possible contact situations.

We investigate the phenomenon of double sudden transitions in geometric quantum correlations for a system consisting of a bare qubit and a qubit locally coupled to its finite-temperature heat environment with an Ohmic spectrum in the framework of stochastic description. Moreover, we explore the possibility of protecting the geometric discord between the two qubits and prolonging the time during which the geometric discord remains constant by applying Bang-Bang pulses.

Polygonal terrain patterns commonly occur in periglacial regions of the Earth, where seasonal processes of freezing and thawing cause the soil to expand and contract, leading to the formation and growth of cracks. Understanding the formation of this type of networks on the Earth and tracing their evolution (including differentiating ages of formation) can provide us with many insights into the history of similar patterns on Mars, in whose surface they occupy vast extensions, most likely due to the presence of frozen water in the soil. Thus, analogue studies of this type of structure on the Earth are important. In this work, we describe the geometric and topologic characteristics of a number of networks of ice-wedge polygons occurring in a coastal valley, the Adventdalen, on the Norwegian archipelago of Svalbard, in the Arctic, at 78° N. The aim of the study is to try and find the similarities and differences between them and to relate those with factors such as soil characteristics and topography. Given the logistic problems in conducting a complete on site study of all those networks, spread out over many kilometers, the study was conducted through the analysis of remotely sensed imagery: 53 images (four-band RGB+NIR and 0.2 m/pixel of spatial resolution), acquired by the Norwegian Polar Institute in 2009 during their aerial photogrammetric campaign, were purchased and processed. They were orthorectified with an ASTER Global Digital Elevation Model (a product of METI and NASA). Polygonal networks were identified and digitized into a GIS. They occupy a total area of almost 10 km2. The areas covered by the individual networks studied range between 4x103 and 106 m2. Individual polygon sizes vary widely, from 6 to 7x103 m2, with an average of 300 m2. The variation is less pronounced for the networks that are most clearly traceable in the images (which reduces typical errors such as those that create large polygons occupying the area of several smaller ones that go

Sodium borophosphate glasses exhibit intriguing mixed network former effect, with the nonlinear compositional dependence of their glass transition temperature as one of the most typical examples. In this paper, we establish the widely applicable topological constraint model of sodium borophosphate mixed network former glasses to explain the relationship between the internal structure and nonlinear changes of glass transition temperature. The application of glass topology network was discussed in detail in terms of the unified methodology for the quantitative distribution of each coordinated boron and phosphorus units and glass transition temperature dependence of atomic constraints. An accurate prediction of composition scaling of the glass transition temperature was obtained based on topological constraint model.

The Berezinskii-Kosterlitz-Thouless (BKT) phase transition drives the unbinding of topological defects in many two-dimensional systems. In the two-dimensional Coulomb gas, it corresponds to an insulator-conductor transition driven by charge deconfinement. We investigate the global topological properties of this transition, both analytically and by numerical simulation, using a lattice-field description of the two-dimensional Coulomb gas on a torus. The BKT transition is shown to be an ergodicity breaking between the topological sectors of the electric field, which implies a definition of topological order in terms of broken ergodicity. The breakdown of local topological order at the BKT transition leads to the excitation of global topological defects in the electric field, corresponding to different topological sectors. The quantized nature of these classical excitations, and their strict suppression by ergodicity breaking in the low-temperature phase, afford striking global signatures of topological-sector fluctuations at the BKT transition. We discuss how these signatures could be detected in experiments on, for example, magnetic films and cold-atom systems.

We study superconducting states in the presence of spin-orbital coupling and Zeeman field. It is found that a phase transition from a Fulde-Ferrell-Larkin-Ovchinnikov state to the topological superconducting state occurs upon increasing the spin-orbital coupling. The nature of this topological phase transition and its critical property are investigated numerically. Physical properties of the topological superconducting phase are also explored. Moreover, the local density of states is calculated, through which the topological feature may be tested experimentally. PMID:24918901

The topology of a topological material can be encoded in its surface states. These surface states can only be removed by a bulk topological quantum phase transition into a trivial phase. Here we use photoemission spectroscopy to image the formation of protected surface states in a topological insulator as we chemically tune the system through a topologicaltransition. Surprisingly, we discover an exotic spin-momentum locked, gapped surface state in the trivial phase that shares many important properties with the actual topological surface state in anticipation of the change of topology. Using a spin-resolved measurement, we show that apart from a surface bandgap these states develop spin textures similar to the topological surface states well before the transition. Our results offer a general paradigm for understanding how surface states in topological phases arise from a quantum phase transition and are suggestive for the future realization of Weyl arcs, condensed matter supersymmetry and other fascinating phenomena in the vicinity of a quantum criticality. PMID:25882717

The topology of a topological material can be encoded in its surface states. These surface states can only be removed by a bulk topological quantum phase transition into a trivial phase. Here we use photoemission spectroscopy to image the formation of protected surface states in a topological insulator as we chemically tune the system through a topologicaltransition. Surprisingly, we discover an exotic spin-momentum locked, gapped surface state in the trivial phase that shares many important properties with the actual topological surface state in anticipation of the change of topology. Using a spin-resolved measurement, we show that apart from a surface bandgap these states develop spin textures similar to the topological surface states well before the transition. Our results offer a general paradigm for understanding how surface states in topological phases arise from a quantum phase transition and are suggestive for the future realization of Weyl arcs, condensed matter supersymmetry and other fascinating phenomena in the vicinity of a quantum criticality. PMID:25882717

The topology of a topological material can be encoded in its surface states. These surface states can only be removed by a bulk topological quantum phase transition into a trivial phase. Here we use photoemission spectroscopy to image the formation of protected surface states in a topological insulator as we chemically tune the system through a topologicaltransition. Surprisingly, we discover an exotic spin-momentum locked, gapped surface state in the trivial phase that shares many important properties with the actual topological surface state in anticipation of the change of topology. Using a spin-resolved measurement, we show that apart from amore » surface bandgap these states develop spin textures similar to the topological surface states well before the transition. Our results provide a general paradigm for understanding how surface states in topological phases arise from a quantum phase transition and are suggestive for the future realization of Weyl arcs, condensed matter supersymmetry and other fascinating phenomena in the vicinity of a quantum criticality.« less

The topology of a topological material can be encoded in its surface states. These surface states can only be removed by a bulk topological quantum phase transition into a trivial phase. Here we use photoemission spectroscopy to image the formation of protected surface states in a topological insulator as we chemically tune the system through a topologicaltransition. Surprisingly, we discover an exotic spin-momentum locked, gapped surface state in the trivial phase that shares many important properties with the actual topological surface state in anticipation of the change of topology. Using a spin-resolved measurement, we show that apart from a surface bandgap these states develop spin textures similar to the topological surface states well before the transition. Our results provide a general paradigm for understanding how surface states in topological phases arise from a quantum phase transition and are suggestive for the future realization of Weyl arcs, condensed matter supersymmetry and other fascinating phenomena in the vicinity of a quantum criticality.

The topology of a topological material can be encoded in its surface states. These surface states can only be removed by a bulk topological quantum phase transition into a trivial phase. Here we use photoemission spectroscopy to image the formation of protected surface states in a topological insulator as we chemically tune the system through a topologicaltransition. Surprisingly, we discover an exotic spin-momentum locked, gapped surface state in the trivial phase that shares many important properties with the actual topological surface state in anticipation of the change of topology. Using a spin-resolved measurement, we show that apart from a surface bandgap these states develop spin textures similar to the topological surface states well before the transition. Our results offer a general paradigm for understanding how surface states in topological phases arise from a quantum phase transition and are suggestive for the future realization of Weyl arcs, condensed matter supersymmetry and other fascinating phenomena in the vicinity of a quantum criticality.

This article presents a versatile, rigorous, and efficient methodology for extracting various geometric and topological parameters of 3D discrete porous media. The new approach takes advantage of the morphological skeleton of the pore structure-a lower dimensional representation of the pore space akin to the topological "deformation retract". The skeleton is derived by a fully parallel thinning algorithm that fulfils two essential requirements: it generates a medial axis and preserves the connectivity of the pore space. Topological analysis is accomplished by classifying all skeleton points as node or link (branch) points according to the concept of lambda-adjacency in 3D discrete space. In this manner, node coordination number and link length distributions are directly obtained from the skeleton. Pore necks (throats) are identified through a search for minima in the hydraulic radius of individual pore space channels outlined by skeleton links. In addition to the determination of the size distribution of the constrictions (pore necks) that control nonwetting phase invasion, improved estimates of the distributions of effective hydraulic and electric conductivity of individual pore space channels are obtained. Furthermore, erection of planes at the location of pore necks results in partitioning of the pore space into its constituent pores. This enables the characterization of the pore space in terms of a pore volume distribution. The new methodology is illustrated by application to a regular cubic pore network and irregularly shaped 2D and 3D pore networks generated by stochastic simulation. In the latter case, important new results are obtained concerning the sensitivity of geometric and topological properties of the microstructure to the parameters of stochastic simulation, namely, the porosity and correlation function. It is found that model porous media reconstructed from the same porosity and correlation function can exhibit marked differences in geometry and

III in AgO. Another interesting aspect of transition metal oxides is their topological properties that are attracting much attention in recent years. The semi-Dirac point, first discovered by Pardo et al and later modeled by Banerjee et al, has linear dispersion along the diagonal and quadratic dispersion perpendicular to the diagonal. In this thesis, we revisit the tight-binding Hamiltonian proposed by Banerjee and extend it to include the effects of external magnetic field on the energy spectrum and topological properties. We also discuss the forms of effective model Hamiltonians that can generate non-zero Berry phase. First principles calculations have been successful in guiding the experimental search for high Tc superconductors, the most recent example being high Tc (203K) superconductor H 3S under pressure (200GPa). The superconductivity of H3S was first predicted by Duan et al using DFT combined with structure optimization algorithms and validated soon after. Though elemental hydrogen was predicted to metallize under pressure in 1930, it was not realized until recently that hydrogen based compounds rather than pure hydrogen atoms are better candidates for high Tc superconductors. In this thesis, we carried out first principle calculations to study the unusual van Hove singularities located near the Fermi level that lead to a sharp peak, and analyzed the hybridization between sulfur and hydrogen states by constructing a tight-binding model.

Using first-principles calculations, we show that topological quantum phase transitions are driven by external electric fields in thin films of Sb2Te3. The film, as the applied electric field normal to its surface increases, is transformed from a normal insulator to a topological insulator or vice versa depending on the film thickness. We identify the band topology by directly calculating the invariant from electronic wave functions. The dispersion of edge states is also found to be consistent with the bulk band topology in view of the bulk-boundary correspondence. We present possible applications of the topological phase transition as an on/off switch of the topologically protected edge states in nano-scale devices. PMID:22203972

We investigate the mechanism by which topological defects form in first-order phase transitions with a charged-order parameter. We show how thick superconductor vortices and heavy cosmic strings form by trapping of magnetic flux. In an external magnetic field, intermediate objects such as strips and membranes of magnetic flux and chains of single winding defects are produced. At non-zero temperature, a variety of spontaneous defects of different winding numbers arise. In cosmology, our results mean that the magnetic flux thermal fluctuations get trapped in a primordial multi-tension string network. The mechanism may also apply to the production of cosmic-like strings in brane collisions. In a thin type-I superconductor film, flux strips are found to be meta-stable while thick vortices are stable up to some critical value of the winding number which increases with the thickness of the film. In addition, a non-dissipative Josephson-like current is obtained across the strips of quantized magnetic flux.

Many phenomena in solid-state physics can be understood in terms of their topological properties. Recently, controlled protocols of quantum walk (QW) are proving to be effective simulators of such phenomena. Here we report the realization of a photonic QW showing both the trivial and the non-trivial topologies associated with chiral symmetry in one-dimensional (1D) periodic systems. We find that the probability distribution moments of the walker position after many steps can be used as direct indicators of the topological quantum transition: while varying a control parameter that defines the system phase, these moments exhibit a slope discontinuity at the transition point. Numerical simulations strongly support the conjecture that these features are general of 1D topological systems. Extending this approach to higher dimensions, different topological classes, and other typologies of quantum phases may offer general instruments for investigating and experimentally detecting quantum transitions in such complex systems. PMID:27102945

Many phenomena in solid-state physics can be understood in terms of their topological properties. Recently, controlled protocols of quantum walk (QW) are proving to be effective simulators of such phenomena. Here we report the realization of a photonic QW showing both the trivial and the non-trivial topologies associated with chiral symmetry in one-dimensional (1D) periodic systems. We find that the probability distribution moments of the walker position after many steps can be used as direct indicators of the topological quantum transition: while varying a control parameter that defines the system phase, these moments exhibit a slope discontinuity at the transition point. Numerical simulations strongly support the conjecture that these features are general of 1D topological systems. Extending this approach to higher dimensions, different topological classes, and other typologies of quantum phases may offer general instruments for investigating and experimentally detecting quantum transitions in such complex systems. PMID:27102945

Many phenomena in solid-state physics can be understood in terms of their topological properties. Recently, controlled protocols of quantum walk (QW) are proving to be effective simulators of such phenomena. Here we report the realization of a photonic QW showing both the trivial and the non-trivial topologies associated with chiral symmetry in one-dimensional (1D) periodic systems. We find that the probability distribution moments of the walker position after many steps can be used as direct indicators of the topological quantum transition: while varying a control parameter that defines the system phase, these moments exhibit a slope discontinuity at the transition point. Numerical simulations strongly support the conjecture that these features are general of 1D topological systems. Extending this approach to higher dimensions, different topological classes, and other typologies of quantum phases may offer general instruments for investigating and experimentally detecting quantum transitions in such complex systems.

Using a combination of density functional theory, tight-binding models, and Hartree-Fock theory, we predict topological phases with and without time-reversal symmetry breaking in oxide heterostructures. We consider both heterostructures containing light transition metal ions and those containing heavy transition metal ions. We find that the (111) growth direction naturally leads to favorable conditions for topological phases in both perovskite structures and pyrochlore structures. For the case of light transition metal elements, Hartree-Fock theory predicts the spin-orbit coupling is effectively enhanced by on-site multiple-orbital interactions and may drive the system through a topological phase transition, while heavy elements with intrinsically large spin-orbit coupling require much weaker or even vanishing electron interactions to bring about a topological phase.

We investigate the topological phase transitions in a two-dimensional time-reversal invariant topological superconductor in the presence of a Zeeman field. Based on the spin Chern number theory, we find that the system exhibits a number of topologically distinct phases with changing the out-of-plane component of the Zeeman field, including a quantum spin Hall-like phase, quantum anomalous Hall-like phases with total Chern number C = −2, −1, 1 and 2, and a topologically trivial superconductor phase. The BdG band gap closes at each boundary of the phase transitions. Furthermore, we demonstrate that the zero bias conductance provides clear transport signatures of the different topological phases, which are robust against symmetry-breaking perturbations. PMID:27148675

We investigate the topological phase transitions in a two-dimensional time-reversal invariant topological superconductor in the presence of a Zeeman field. Based on the spin Chern number theory, we find that the system exhibits a number of topologically distinct phases with changing the out-of-plane component of the Zeeman field, including a quantum spin Hall-like phase, quantum anomalous Hall-like phases with total Chern number C = -2, -1, 1 and 2, and a topologically trivial superconductor phase. The BdG band gap closes at each boundary of the phase transitions. Furthermore, we demonstrate that the zero bias conductance provides clear transport signatures of the different topological phases, which are robust against symmetry-breaking perturbations. PMID:27148675

The importance of models with an exact solution for the study of materials with non-trivial topological properties has been extensively demonstrated. The Kitaev model plays a guiding role in the search for Majorana modes in condensed matter systems. Also, the sp-chain with an anti-symmetric mixing among the s and p bands is a paradigmatic example of a topological insulator with well understood properties. Interestingly, these models share the same universality class for their topological quantum phase transitions. In this work we study a two-band model of spinless fermions with attractive inter-band interactions. We obtain its zero temperature phase diagram, which presents a rich variety of phases including a Weyl superconductor and a topological insulator. The transition from the topological to the trivial superconducting phase has critical exponents different from those of Kitaev's model. PMID:26440940

Just as the topology of the Fermi surface defines the properties of the free electrons in metals and semiconductors, the geometry of the iso-frequency surface in the phase space of the propagating electromagnetic waves, determines the optical properties of the corresponding optical materials. Furthermore, in the direct analog to the Lifshitz transition in condensed matter physics, a change in the topology of iso-frequency surface has a dramatic effect on the emission, propagation and scattering of the electromagnetic waves. Here, we uncover a new class of such optical topologicaltransitions in metamaterials, induced by the non-locality of the electromagnetic response inherent to these composites.

Just as the topology of the Fermi surface defines the properties of the free electrons in metals and semiconductors, the geometry of the iso-frequency surface in the phase space of the propagating electromagnetic waves, determines the optical properties of the corresponding optical materials. Furthermore, in the direct analog to the Lifshitz transition in condensed matter physics, a change in the topology of iso-frequency surface has a dramatic effect on the emission, propagation and scattering of the electromagnetic waves. Here, we uncover a new class of such optical topologicaltransitions in metamaterials, induced by the non-locality of the electromagnetic response inherent to these composites. PMID:26670600

Just as the topology of the Fermi surface defines the properties of the free electrons in metals and semiconductors, the geometry of the iso-frequency surface in the phase space of the propagating electromagnetic waves, determines the optical properties of the corresponding optical materials. Furthermore, in the direct analog to the Lifshitz transition in condensed matter physics, a change in the topology of iso-frequency surface has a dramatic effect on the emission, propagation and scattering of the electromagnetic waves. Here, we uncover a new class of such optical topologicaltransitions in metamaterials, induced by the non-locality of the electromagnetic response inherent to these composites. PMID:26670600

Although the topological order is known as a quantum order in quantum many-body systems, it seems that there is not a one-to-one correspondence between topological phases and quantum phases. As a well-known example, it has been shown that all one-dimensional (1D) quantum phases are topologically trivial [X. Chen et al., Phys. Rev. B 90, 035117 (2014), 10.1103/PhysRevB.90.035117]. By such facts, it seems a challenging task to understand when a quantum phase transition between different topological models necessarily reveals different topological classes of them. In this paper, we make an attempt to consider this problem by studying a phase transition between two different quantum phases which have a universal topological phase. We define a Hamiltonian as interpolation of the toric code model with Z2 topological order and the color code model with Z2×Z2 topological order on a hexagonal lattice. We show such a model is exactly mapped to many copies of 1D quantum Ising model in transverse field by rewriting the Hamiltonian in a new complete basis. Consequently, we show that the universal topological phase of the color code model and the toric code model reflects in the 1D nature of the phase transition. We also consider the expectation value of Wilson loops by a perturbative calculation and show that behavior of the Wilson loop captures the nontopological nature of the quantum phase transition. The result on the point of phase transition also shows that the color code model is strongly robust against the toric code model.

Indistinguishable particles in two dimensions can be characterized by anyonic quantum statistics, which is more general than that of bosons or fermions. Anyons emerge as quasiparticles in fractional quantum Hall states and in certain frustrated quantum magnets. Quantum liquids of anyons show degenerate ground states, where the degeneracy depends on the topology of the underlying surface. Here, we present a new type of continuous quantum phase transition in such anyonic quantum liquids, which is driven by quantum fluctuations of the topology. The critical state connecting two anyonic liquids on surfaces with different topologies is reminiscent of the notion of a `quantum foam' with fluctuations on all length scales. This exotic quantum phase transition arises in a microscopic model of interacting anyons for which we present an exact solution in a linear geometry. We introduce an intuitive physical picture of this model that unifies string nets and loop gases, and provide a simple description of topological quantum phases and their phase transitions.

We show that the zero point motion of a vortex in superconducting doped topological insulators leads to significant changes in the electronic spectrum at the topological phase transition in this system. This topological phase transition is tuned by the doping level, and the corresponding effects are manifest in the density of states at energies which are on the order of the vortex fluctuation frequency. Although the electronic energy gap in the spectrum generated by a stationary vortex is but a small fraction of the bulk superconducting gap, the vortex fluctuation frequency may be much larger. As a result, this quantum zero point motion can induce a discontinuous change in the spectral features of the system at the topological vortex phase transition to energies which are well within the resolution of scanning tunneling microscopy. This discontinuous change is exclusive to superconducting systems in which we have a topological phase transition. Moreover, the phenomena studied in this paper present effects of Magnus forces on the vortex spectrum which are not present in the ordinary s -wave superconductors. Finally, we demonstrate explicitly that the vortex in this system is equivalent to a Kitaev chain. This allows for the mapping of the vortex fluctuating scenario in three dimensions into similar one-dimensional situations in which one may search for other novel signatures of topological phase transitions.

Topological insulators (TI) are a class of materials with insulating bulk and metallic surface state, which is the result of band inversion induced by strong spin-orbit coupling (SOC). The transition from topological phase to non-topological phase is of great significance. In theory, topological phase transition is realized by tuning SOC strength. It is characterized by the process of gap closing and reopening. Experimentally it was observed in two systems: TlBi(S1-xSex)2 and (Bi1-xInx)2 Se3 where the transition is realized by varying isovalent elements doping concentration. However, none of the previous studies addressed the impact of disorder, which is inevitable in doped systems. Here, we present a systematic scanning tunneling microscopy/spectroscopy study on (Bi1-xInx)2 Se3 single crystals with different In concentrations across the transition. Our results reveal an electronic inhomogeneity due to the random distribution of In defects which locally suppress the topological surface states. Our study provides a new angle of understanding the topologicaltransition in the presence of strong disorders. This work is supported by NSF DMR-1506618.

By extending the quantum evolution of a scalar field in time-dependent backgrounds to the complex-time plane and transporting the in-vacuum along a closed path, we argue that the geometrictransition from the simple pole at infinity determines the multi-pair production depending on the winding number. We apply the geometrictransition to Schwinger mechanism in the time-dependent vector potential for a constant electric field and to Gibbons-Hawking particle production in the planar coordinates of a de Sitter space.

Topological insulators (TIs) hold great promise for topological quantum computation in solid-state systems. Recently, several groups reported experimental data suggesting that signatures of Majorana modes have been observed in topological insulator Josephson junctions (TIJJs). A prerequisite for the exploration of Majorana physics is to obtain a good understanding of the properties of low-energy Andreev bound states (ABSs) in a material with a topologically nontrivial band structure. Here, we present experimental data and a theoretical analysis demonstrating that the band-structure inversion close to the surface of a TI has observable consequences for supercurrent transport in TIJJs prepared on surface-doped Bi2Se3 thin films. Electrostatic carrier depletion of the film surface leads to an abrupt drop in the critical current of such devices. The effect can be understood as a relocation of low-energy ABSs from a region deeper in the bulk of the material to the more strongly disordered surface, which is driven by the topology of the effective band structure in the presence of surface dopants.

Shape analysis plays an important role in many applications. In particular, in molecular biology, analyzing molecular shapes is essential to the fundamental problem of understanding how molecules interact. This project aims at developing efficient and effective algorithms to characterize and analyze molecular structures using geometric and topological methods. Two main components of this project are (1) developing novel molecular shape descriptors; and (2) identifying and representing meaningful features based on those descriptors. The project also produces accompanying (visualization) software. Results from this project (09/2006-10/2009) include the following publications. We have also set up web-servers for the software developed in this period, so that our new methods are accessible to a broader scientific community. The web sites are given below as well. In this final technical report, we first list publications and software resulted from this project. We then briefly explain the research conducted and main accomplishments during the period of this project.

Extensive studies characterizing Titan present an opportunity to study the atmospheric properties of Titan-like exoplanets. Using an existing model of Titan's atmospheric haze, we computed geometric albedo spectra and effective transit height spectra for six values of the haze production rate (zero haze to twice present) over a wide range of wavelengths (0.2-2 μm). In the geometric albedo spectra, the slope in the UV-visible changes from blue to red when varying the haze production rate values from zero to twice the current Titan value. This spectral feature is the most effective way to characterize the haze production rates. Methane absorption bands in the visible-NIR compete with the absorbing haze, being more prominent for smaller haze production rates. The effective transit heights probe a region of the atmosphere where the haze and gas are optically thin and that is thus not effectively probed by the geometric albedo. The effective transit height decreases smoothly with increasing wavelength, from 376 km to 123 km at 0.2 and 2 μm, respectively. When decreasing the haze production rate, the methane absorption bands become more prominent, and the effective transit height decreases with a steeper slope with increasing wavelength. The slope of the geometric albedo in the UV-visible increases smoothly with increasing haze production rate, while the slope of the effective transit height spectra is not sensitive to the haze production rate other than showing a sharp rise when the haze production rate increases from zero. We conclude that geometric albedo spectra provide the most sensitive indicator of the haze production rate and the background Rayleigh gas. Our results suggest that important and complementary information can be obtained from the geometric albedo and motivates improvements in the technology for direct imaging of nearby exoplanets.

We propose a series of simple two-dimensional (2D) lattice interacting fermion models that we demonstrate at low energy describe bosonic symmetry-protected topological (SPT) states and quantum phase transitions between them. This is because due to interaction, the fermions are gapped both at the boundary of the SPT states and at the bulk quantum phase transition, thus these models at low energy can be described completely by bosonic degrees of freedom. We show that the bulk of these models is described by a Sp (N ) principal chiral model with a topological Θ term, whose boundary is described by a Sp (N ) principal chiral model with a Wess-Zumino-Witten term at level 1. The quantum phase transition between SPT states in the bulk is tuned by a particular interaction term, which corresponds to tuning Θ in the field theory, and the phase transition occurs at Θ =π . The simplest version of these models with N =1 is equivalent to the familiar O(4) nonlinear sigma model (NLSM) with a topological term, whose boundary is a (1 +1 )D conformal field theory with central charge c =1 . After breaking the O(4) symmetry to its subgroups, this model can be viewed as bosonic SPT states with U(1), or Z2 symmetries, etc. All of these fermion models, including the bulk quantum phase transitions, can be simulated with the determinant quantum Monte Carlo method without the sign problem. Recent numerical results strongly suggest that the quantum disordered phase of the O(4) NLSM with precisely Θ =π is a stable (2 +1 )D conformal field theory with gapless bosonic modes.

NASA’s Kepler Space Telescope has successfully discovered thousands of exoplanet candidates using the transit method, including hundreds of stars with multiple transiting planets. In order to estimate the frequency of these valuable systems, it is essential to account for the unique geometric probabilities of detecting multiple transiting extrasolar planets around the same parent star. In order to improve on previous studies that used numerical methods, we have constructed an efficient, semi-analytical algorithm called the Computed Occurrence of Revolving Bodies for the Investigation of Transiting Systems (CORBITS), which, given a collection of conjectured exoplanets orbiting a star, computes the probability that any particular group of exoplanets can be observed to transit. The algorithm applies theorems of elementary differential geometry to compute the areas bounded by circular curves on the surface of a sphere. The implemented algorithm is more accurate and orders of magnitude faster than previous algorithms, based on comparisons with Monte Carlo simulations. We use CORBITS to show that the present solar system would only show a maximum of three transiting planets, but that this varies over time due to dynamical evolution. We also used CORBITS to geometrically debias the period ratio and mutual Hill sphere distributions of Kepler's multi-transiting planet candidates, which results in shifting these distributions toward slightly larger values. In an Appendix, we present additional semi-analytical methods for determining the frequency of exoplanet mutual events, i.e., the geometric probability that two planets will transit each other (planet–planet occultation, relevant to transiting circumbinary planets) and the probability that this transit occurs simultaneously as they transit their star. The CORBITS algorithms and several worked examples are publicly available.

We study the interplay of topological band structure and conventional magnetic long-range order in spinful Haldane model with on-site repulsive interaction. Using the dynamical cluster approximation with clusters of up to 24 sites we find evidence of a first-order phase transition from a Chern insulator at weak coupling to a topologically trivial antiferromagnetic insulator at strong coupling. These results call into question a previously found intermediate state with coexisting topological character and antiferromagnetic long-range order. Experimentally measurable signatures of the first-order transition include hysteretic behavior of the double occupancy, single-particle excitation gap, and nearest neighbor spin-spin correlations. This first-order transition is contrasted with a continuous phase transition from the conventional band insulator to the antiferromagnetic insulator in the ionic Hubbard model on the honeycomb lattice.

We extend the stochastic master equation approach described earlier [J. J. Kozak and R. Davidson, J. Chem. Phys. 101, 6101 (1994)] to examine the influence on reaction efficiency of multipolar correlations between a fixed target molecule and a diffusing coreactant, the latter constrained to move on the surface of a host medium (e.g., a colloidal catalyst or molecular organizate) modeled as a Cartesian shell [Euler characteristic, χ=2]. Our most comprehensive results are for processes involving ion pairs, and we find that there exists a transition between two qualitatively different types of behavior in diffusion-reaction space, viz., a regime where the coreactant's motion is totally correlated with respect to the target ion, and a regime where the coreactant's motion is effectively uncorrelated. This behavior emerges both in the situation where correlations between the ion pair are strictly confined to the surface of the host medium or where correlations can be propagated through the host medium. The effects of system size are also examined and comparisons with diffusion-reaction processes taking place on surfaces characterized by Euler characteristic χ=0 are made. In all cases studied, the most dramatic effects on the reaction efficiency are uncovered in the regime where the Onsager (thermalization) length is comparable to the mean displacement of the coreactant, a conclusion consistent with results reported in earlier work.

A jammed packing of frictionless spheres at zero temperature is perfectly specified by the network of contact forces from which mechanical properties can be derived. However, we can alternatively consider a packing as a geometric structure, characterized by a Voronoi tessellation which encodes the local environment around each particle. We find that this local environment characterizes systems both above and below jamming and changes markedly at the transition. A variety of order parameters derived from this tessellation carry signatures of the jamming transition, complete with scaling exponents. Furthermore, we define a real space geometric correlation function which also displays a signature of jamming. Taken together, these results demonstrate the validity and usefulness of a purely geometric approach to jamming. PMID:26611105

Topological superconductors differ from topologically trivial ones due to the presence of topologically protected zero-energy modes. To date, experimental evidence of topological superconductivity in nanostructures has been mainly obtained by measuring the zero-bias conductance peak via tunneling spectroscopy. Here, we propose an alternative and complementary experimental recipe to detect topological phase transitions in these systems. We show in fact that, for a finite-sized system with broken time-reversal symmetry, discontinuities in the Josephson current-phase relation correspond to the presence of zero-energy modes and to a change in the fermion parity of the ground state. Such discontinuities can be experimentally revealed by a characteristic temperature dependence of the current, and can be related to a finite anomalous current at zero phase in systems with broken phase-inversion symmetry.

The phase-dependent bound states (Andreev levels) of a Josephson junction can cross at the Fermi level if the superconducting ground state switches between even and odd fermion parity. The level crossing is topologically protected, in the absence of time-reversal and spin-rotation symmetry, irrespective of whether the superconductor itself is topologically trivial or not. We develop a statistical theory of these topologicaltransitions in an N-mode quantum-dot Josephson junction by associating the Andreev level crossings with the real eigenvalues of a random non-Hermitian matrix. The number of topologicaltransitions in a 2π phase interval scales as √[N], and their spacing distribution is a hybrid of the Wigner and Poisson distributions of random-matrix theory. PMID:23909353

We present a holographic model of a topological Weyl semimetal. A key ingredient is a time-reversal breaking parameter and a mass deformation. Upon varying the ratio of mass to time-reversal breaking parameter the model undergoes a quantum phase transition from a topologically nontrivial semimetal to a trivial one. The topological nontrivial semimetal is characterized by the presence of an anomalous Hall effect. The results can be interpreted in terms of the holographic renormalization group (RG) flow leading to restoration of time reversal at the end point of the RG flow in the trivial phase. PMID:26967408

We study the formation of transportation networks of the true slime mold Physarum polycephalum after fragmentation by shear. Small fragments, called microplasmodia, fuse to form macroplasmodia in a percolation transition. At this topological phase transition, one single giant component forms, connecting most of the previously isolated microplasmodia. Employing the configuration model of graph theory for small link degree, we have found analytically an exact solution for the phase transition. It is generally applicable to percolation as seen, e.g., in vascular networks.

All the possible thermal equilibrium states of geometrically thin alpha-disks around stellar-mass black holes are presented. A (vertically) one-zone disk model is employed and it is assumed that a main energy source is viscous heating of protons and that cooling is due to bremsstrahlung and Compton scattering. There exist various branches of the thermal equilibrium solution, depending on whether disks are effectively optically thick or thin, radiation pressure-dominated or gas pressure-dominated, composed of one-temperature plasmas or of two-temperature plasmas, and with high concentration of e(+)e(-) pairs or without pairs. The thermal equilibrium curves at high temperatures (greater than or approximately equal to 10 exp 8 K) are substantially modified by the presence of e(+)e(-) pairs. The thermal stability of these branches are examined.

We are concerned with singularities of the shock fronts of converging perturbed shock waves. Our considerations are based on Whitham's theory of geometrical shock dynamics. The recently developed method of local analysis is applied in order to determine generic singularities. In this case the solutions of partial differential equations describing the geometry of the shock fronts are presented as families of smooth maps with state variables and the set of control parameters dependent on Mach number, time and initial conditions. The space of control parameters of the singularities is analysed, the unfoldings describing the deformations of the canonical germs of shock front singularities are found and corresponding bifurcation diagrams are constructed. Research is supported by the Leverhulme Trust, Grant Number RPG-2012-568.

Molecular dynamics simulations of small Cu nanoparticles using three different interatomic potentials at rising temperature indicate that small nanoparticles can undergo solid-solid structural transitions through a direct geometrical conversion route. The direct geometrical conversion can happen for cuboctahedral nanoparticles, which turn into an icosahedra shape: one diagonal of the square faces contracts, and the faces are folded along the diagonal to give rise to two equilateral triangles. The transition is a kinetic process that cannot be fully explained through an energetic point of view. It has low activation energy and fast reaction time in the simulations. The transition mechanism is via the transmission of shear waves initiated from the particle surface and does not involve dislocation activity.

Molecular dynamics simulations of small Cu nanoparticles using three different interatomic potentials at rising temperature indicate that small nanoparticles can undergo solid-solid structural transitions through a direct geometrical conversion route. The direct geometrical conversion can happen for cuboctahedral nanoparticles, which turn into an icosahedra shape: one diagonal of the square faces contracts, and the faces are folded along the diagonal to give rise to two equilateral triangles. The transition is a kinetic process that cannot be fully explained through an energetic point of view. It has low activation energy and fast reaction time in the simulations. The transition mechanism is via the transmission of shear waves initiated from the particle surface and does not involve dislocation activity. PMID:23635145

The method of synthetic gauge potentials opens up a new avenue for our understanding and discovering novel quantum states of matter. We investigate the topological quantum phase transition of Fermi gases trapped in a honeycomb lattice in the presence of a synthetic non-Abelian gauge potential. We develop a systematic fermionic effective field theory to describe a topological quantum phase transition tuned by the non-Abelian gauge potential and explore its various important experimental consequences. Numerical calculations on lattice scales are performed to compare with the results achieved by the fermionic effective field theory. Several possible experimental detection methods of topological quantum phase transition are proposed. In contrast to condensed matter experiments where only gauge invariant quantities can be measured, both gauge invariant and non-gauge invariant quantities can be measured by experimentally generating various non-Abelian gauges corresponding to the same set of Wilson loops. PMID:23846153

We investigate the role of short-ranged electron-electron interactions in a paradigmatic model of three-dimensional topological insulators, using dynamical mean-field theory and focusing on nonmagnetically ordered solutions. The noninteracting band structure is controlled by a mass term M , whose value discriminates between three different insulating phases, a trivial band insulator and two distinct topologically nontrivial phases. We characterize the evolution of the transitions between the different phases as a function of the local Coulomb repulsion U and find a remarkable dependence of the U -M phase diagram on the value of the local Hund's exchange coupling J . However, regardless of the value of J , following the evolution of the topologicaltransition line between a trivial band insulator and a topological insulator, we find a critical value of U separating a continuous transition from a first-order one. When the Hund's coupling is significant, a Mott insulator is stabilized at large U . In proximity of the Mott transition we observe the emergence of an anomalous "Mott-like" strong topological insulator state.

In recent years, a low pressure transition around P3 GPa exhibited by the A2B3-type 3D topological insulators is attributed to an electronic topologicaltransition (ETT) for which there is no direct evidence either from theory or experiments. We address this phase transition and other transitions at higher pressure in bismuth selenide (Bi2Se3) using Raman spectroscopy at pressure up to 26.2 GPa. We see clear Raman signatures of an isostructural phase transition at P2.4 GPa followed by structural transitions at ∼ 10 GPa and 16 GPa. First-principles calculations reveal anomalously sharp changes in the structural parameters like the internal angle of the rhombohedral unit cell with a minimum in the c/a ratio near P3 GPa. While our calculations reveal the associated anomalies in vibrational frequencies and electronic bandgap, the calculated Z2 invariant and Dirac conical surface electronic structure remain unchanged, showing that there is no change in the electronic topology at the lowest pressure transition. PMID:26881905

In recent years, a low pressure transition around P∼ 3 GPa exhibited by the {{A}2}{{B}3} -type 3D topological insulators is attributed to an electronic topologicaltransition (ETT) for which there is no direct evidence either from theory or experiments. We address this phase transition and other transitions at higher pressure in bismuth selenide (Bi2Se3) using Raman spectroscopy at pressure up to 26.2 GPa. We see clear Raman signatures of an isostructural phase transition at P∼ 2.4 GPa followed by structural transitions at ∼10 GPa and 16 GPa. First-principles calculations reveal anomalously sharp changes in the structural parameters like the internal angle of the rhombohedral unit cell with a minimum in the c/a ratio near P∼ 3 GPa. While our calculations reveal the associated anomalies in vibrational frequencies and electronic bandgap, the calculated {{{Z}}2} invariant and Dirac conical surface electronic structure remain unchanged, showing that there is no change in the electronic topology at the lowest pressure transition.

The mechanism for the fast switching between amorphous, metastable, and crystalline structures in chalcogenide phase-change materials has been a long-standing puzzle. Based on first-principles calculations, we study the atomic and electronic properties of metastable Ge2Sb2Te5 and investigate the atomic disorder to understand the transition between crystalline hexagonal and cubic structures. In addition, we study the topological insulating property embedded in these compounds and its evolution upon structural changes and atomic disorder. We also discuss the role of the surface-like states arising from the topological insulating property in the metal-insulator transition observed in the hexagonal structure.

A new type of collective excitations, due to the topology of a complex random network that can be characterized by a fractal dimension DF, is investigated. We show analytically that these excitations generate phase transitions due to the non-periodic topology of the DF > 1 complex network. An Ising system, with long range interactions, is studied in detail to support the claim. The analytic treatment is possible because the evaluation of the partition function can be decomposed into closed factor loops, in spite of the architectural complexity. The removal of the infrared divergences leads to an unconventional phase transition, with spin correlations that are robust against thermal fluctuations.

Topological insulators (TIs) are bulk insulators with exotic ‘topologically protected’ surface conducting modes. It has recently been pointed out that when stacked together, interactions between surface modes can induce diverse phases including the TI, Dirac semimetal, and Weyl semimetal. However, currently a full experimental understanding of the conditions under which topological modes interact is lacking. Here, working with multilayers of the TI Sb2Te3 and the band insulator GeTe, we provide experimental evidence of multiple topological modes in a single Sb2Te3-GeTe-Sb2Te3 structure. Furthermore, we show that reducing the thickness of the GeTe layer induces a phase transition from a Dirac-like phase to a gapped phase. By comparing different multilayer structures we demonstrate that this transition occurs due to the hybridisation of states associated with different TI films. Our results demonstrate that the Sb2Te3-GeTe system offers strong potential towards manipulating topological states as well as towards controlledly inducing various topological phases. PMID:27291288

Topological insulators (TIs) are bulk insulators with exotic 'topologically protected' surface conducting modes. It has recently been pointed out that when stacked together, interactions between surface modes can induce diverse phases including the TI, Dirac semimetal, and Weyl semimetal. However, currently a full experimental understanding of the conditions under which topological modes interact is lacking. Here, working with multilayers of the TI Sb2Te3 and the band insulator GeTe, we provide experimental evidence of multiple topological modes in a single Sb2Te3-GeTe-Sb2Te3 structure. Furthermore, we show that reducing the thickness of the GeTe layer induces a phase transition from a Dirac-like phase to a gapped phase. By comparing different multilayer structures we demonstrate that this transition occurs due to the hybridisation of states associated with different TI films. Our results demonstrate that the Sb2Te3-GeTe system offers strong potential towards manipulating topological states as well as towards controlledly inducing various topological phases. PMID:27291288

Topological insulators (TIs) are bulk insulators with exotic ‘topologically protected’ surface conducting modes. It has recently been pointed out that when stacked together, interactions between surface modes can induce diverse phases including the TI, Dirac semimetal, and Weyl semimetal. However, currently a full experimental understanding of the conditions under which topological modes interact is lacking. Here, working with multilayers of the TI Sb2Te3 and the band insulator GeTe, we provide experimental evidence of multiple topological modes in a single Sb2Te3-GeTe-Sb2Te3 structure. Furthermore, we show that reducing the thickness of the GeTe layer induces a phase transition from a Dirac-like phase to a gapped phase. By comparing different multilayer structures we demonstrate that this transition occurs due to the hybridisation of states associated with different TI films. Our results demonstrate that the Sb2Te3-GeTe system offers strong potential towards manipulating topological states as well as towards controlledly inducing various topological phases.

It is expected the interplay between non-trivial band topology and strong electron correlation will lead to very rich physics. Thus a controlled study of the competition between topology and correlation is of great interest. Here, employing large-scale quantum Monte Carlo simulations, we provide a concrete example of the Kane-Mele-Hubbard model on an AA stacking bilayer honeycomb lattice with inter-layer antiferromagnetic interaction. Our simulation identified several different phases: a quantum spin-Hall insulator (QSH), a xy-plane antiferromagnetic Mott insulator (xy-AFM) and an inter-layer dimer-singlet insulator (dimer-singlet). Most importantly, a bona fide topological phase transition between the QSH and the dimer-singlet insulators, purely driven by the inter-layer antiferromagnetic interaction is found. At the transition, the spin and charge gap of the system close while the single-particle excitations remain gapped, which means that this transition has no mean field analogue and it can be viewed as a transition between bosonic SPT states. At one special point, this transition is described by a (2+1)d O(4) nonlinear sigma model with exact SO(4) symmetry, and a topological term at theta=p. Relevance of this work towards more general interacting SPT states is discussed.

Geometric entanglement (GE), as a measure of multipartite entanglement, has been investigated as a universal tool to detect phase transitions in quantum many-body lattice models. In this paper we outline a systematic method to compute GE for two-dimensional (2D) quantum many-body lattice models based on the translational invariant structure of infinite projected entangled pair state (iPEPS) representations. By employing this method, the q -state quantum Potts model on the square lattice with q ∈{2 ,3 ,4 ,5 } is investigated as a prototypical example. Further, we have explored three 2D Heisenberg models: the antiferromagnetic spin-1/2 X X X and anisotropic X Y X models in an external magnetic field, and the antiferromagnetic spin-1 X X Z model. We find that continuous GE does not guarantee a continuous phase transition across a phase transition point. We observe and thus classify three different types of continuous GE across a phase transition point: (i) GE is continuous with maximum value at the transition point and the phase transition is continuous, (ii) GE is continuous with maximum value at the transition point but the phase transition is discontinuous, and (iii) GE is continuous with nonmaximum value at the transition point and the phase transition is continuous. For the models under consideration, we find that the second and the third types are related to a point of dual symmetry and a fully polarized phase, respectively.

A sudden quantum quench of a Bloch band from one topological phase toward another has been shown to exhibit an intimate connection with the notion of a dynamical quantum phase transition (DQPT), where the returning probability of the quenched state to the initial state—i.e., the Loschmidt echo—vanishes at critical times {t*}. Analytical results to date are limited to two-band models, leaving the exact relation between topology and DQPT unclear. In this Letter, we show that, for a general multiband system, a robust DQPT relies on the existence of nodes (i.e., zeros) in the wave function overlap between the initial band and the postquench energy eigenstates. These nodes are topologically protected if the two participating wave functions have distinctive topological indices. We demonstrate these ideas in detail for both one and two spatial dimensions using a three-band generalized Hofstadter model. We also discuss possible experimental observations.

A sudden quantum quench of a Bloch band from one topological phase toward another has been shown to exhibit an intimate connection with the notion of a dynamical quantum phase transition (DQPT), where the returning probability of the quenched state to the initial state-i.e., the Loschmidt echo-vanishes at critical times {t^{*}}. Analytical results to date are limited to two-band models, leaving the exact relation between topology and DQPT unclear. In this Letter, we show that, for a general multiband system, a robust DQPT relies on the existence of nodes (i.e., zeros) in the wave function overlap between the initial band and the postquench energy eigenstates. These nodes are topologically protected if the two participating wave functions have distinctive topological indices. We demonstrate these ideas in detail for both one and two spatial dimensions using a three-band generalized Hofstadter model. We also discuss possible experimental observations. PMID:27588874

Until the late 1980s, phases of matter were understood in terms of Landau’s symmetry-breaking theory. Following the discovery of the quantum Hall effect, the introduction of a second class of phases, those with topological order, was necessary. Phase transitions within the first class of phases involve a change in symmetry, whereas those between topological phases require a change in topological order. However, in rare cases, transitions may occur between the two classes, in which the vanishing of the topological order is accompanied by the emergence of a broken symmetry. Here, we report the existence of such a transition in a two-dimensional electron gas hosted by a GaAs/AlGaAs crystal. When tuned by hydrostatic pressure, the ν = 5/2 fractional quantum Hall state, believed to be a prototypical non-Abelian topological phase, gives way to a quantum Hall nematic phase. Remarkably, this nematic phase develops spontaneously, in the absence of any externally applied symmetry-breaking fields.

We consider static, axisymmetric, thick-brane solutions on higher-dimensional, spherically symmetric black hole backgrounds. It was found recently [V. G. Czinner and A. Flachi, Phys. Rev. D 80, 104017 (2009).], that in cases in which the thick brane has more than two spacelike dimensions, perturbative approaches break down around the corresponding thin solutions for Minkowski-type topologies. This behavior is a consequence of the fact that thin solutions are not smooth at the axis, and for a general discussion of possible phase transitions in the system, one needs to use a nonperturbative approach. In the present paper, we provide an exact, numerical solution of the problem both for black hole- and Minkowski-type topologies with an arbitrary number of brane and bulk dimensions. We also illustrate a topology change transition in the system for a five-dimensional brane embedded in a six-dimensional bulk.

At low column-to-particle diameter (or aspect) ratio (d(c)/d(p)) the kinetic column performance is dominated by the transcolumn disorder that arises from the morphological gradient between the more homogeneous, looser packed wall region and the random, dense core. For a systematic analysis of this morphology-dispersion relation we computer-generated a set of confined sphere packings varying three parameters: aspect ratio (d(c)/d(p)=10-30), bed porosity (ɛ=0.40-0.46), and packing homogeneity. Plate height curves were received from simulation of hydrodynamic dispersion in the packings over a wide range of reduced velocities (v=0.5-500). Geometrical measures derived from radial porosity and velocity profiles were insufficient as morphological descriptors of the plate height data. After Voronoi tessellation of the packings, topological information was obtained from the statistical moments of the free Voronoi volume (V(free)) distributions. The radial profile of the standard deviation of the V(free) distributions in the form of an integral measure was identified as a quantitative scalar measure for the transcolumn disorder. The first morphology-dispersion correlation for confined sphere packings deepens our understanding of how the packing microstructure determines the kinetic column performance. PMID:23000179

The Bcl-2 family comprises pro-apoptotic proteins, capable of permeabilizing the mitochondrial membrane, and anti-apoptotic members interacting in an antagonistic fashion to regulate programmed cell death (apoptosis). They offer potential therapeutic targets to re-engage cellular suicide in tumor cells but the extensive network of implicated protein-protein interactions has impeded full understanding of the decision pathway. We show, using synchrotron x-ray diffraction, that pro-apoptotic proteins interact with mitochondrial-like model membranes to generate saddle-splay (negative Gaussian) curvature topologically required for pore formation, while anti-apoptotic proteins can deactivate curvature generation by molecules drastically different from Bcl-2 family members and offer evidence for membrane-curvature mediated interactions general enough to affect very disparate systems.

for investigation of topologies of structural units. • The method of orientation matrices was applied to distinguish geometrical isomers. • The flexibility of structural complexes specifies the undulation of layered structural units.

We demonstrate that the Higgs mechanism in three-dimensional topological superconductors exhibits unique features with experimentally observable consequences. The Higgs model we discuss has two superconducting components and an axionlike magnetoelectric term with the phase difference of the superconducting order parameters playing the role of the axion field. Due to this additional term, quantum electromagnetic and phase fluctuations lead to a robust topologically nontrivial state that holds also in the presence of interactions. In this sense, we show that the renormalization flow of the topologically nontrivial phase cannot be continuously deformed into a topologically nontrivial one. One consequence of our analysis of quantum critical fluctuations is the possibility of having a first-order phase transition in the bulk and a second-order phase transition on the surface. We also explore another consequence of the axionic Higgs electrodynamics, namely, the anomalous Hall effect. In the low-frequency London regime an anomalous Hall effect is induced in the presence of an applied electric field parallel to the surface. This anomalous Hall current is induced by a Lorentz-like force arising from the axion term, and it involves the relative superfluid velocity of the superconducting components. The anomalous Hall current has a negative sign, a situation reminiscent of but quite distinct in physical origin from the anomalous Hall effect observed in high-Tc superconductors. In contrast to the latter, the anomalous Hall effect in topological superconductors is nondissipative and occurs in the absence of vortices.

Dirac semimetals host three-dimensional (3D) Dirac fermion states in the bulk of crystalline solids, which can be viewed as 3D analogs of graphene. Owing to their relativistic spectrum and unique topological character, these materials hold great promise for fundamental-physics exploration and practical applications. Particularly, they are expected to be ideal parent compounds for engineering various other topological states of matter. In this report, we investigate the possibility to induce and control the topological quantum spin Hall phase in a Dirac semimetal thin film by using a vertical electric field. We show that through the interplay between the quantum confinement effect and the field-induced coupling between sub-bands, the sub-band gap can be tuned and inverted. During this process, the system undergoes a topological phase transition between a trivial band insulator and a quantum spin Hall insulator. Consequently, one can switch the topological edge channels on and off by purely electrical means, making the system a promising platform for constructing topological field effect transistors. PMID:26420343

The canonical Su-Schrieffer-Heeger (SSH) array is one of the basic geometries that have spurred significant interest in topological band-gap modes. Here, we show that the judicious inclusion of third-order Kerr nonlinearities in SSH arrays opens rich physics in topological insulators, including the possibility of supporting self-induced topologicaltransitions, as a function of the applied intensity. We highlight the emergence of a class of topological solutions in nonlinear SSH arrays localized at the array edges and with unusual properties. As opposed to their linear counterparts, these nonlinear states decay to a plateau of nonzero amplitude inside the array, highlighting the local nature of topologically nontrivial band gaps in nonlinear systems. We study the conditions under which these states can be excited and their temporal dynamics as a function of the applied excitation, paving the way to interesting directions in the physics of topological edge states with robust propagation properties based on nonlinear interactions in suitably designed periodic arrays.

We study the gate-voltage modulated electronic properties of hexagonal boron-nitride bilayers with two different stacking structures in the presence of intrinsic and Rashba spin-orbit interactions. Our analytical results show that there are striking cooperation effects arising from the spin-orbit interactions and the interlayer bias voltage. For realizing topological phase transition, in contrast to a gated graphene bilayer for increasing its energy gap, the energy gap of a boron-nitride bilayer is significantly reduced by an applied gate voltage. For the AA stacking-bilayer which has the inversion symmetry, a strong topological phase is found, and there is an interesting reentrant behavior from a normal phase to a topological phase and then to a normal phase again, characterized by the topological index. Therefore, the gate voltage modulated AA-boron nitride bilayer can be taken as a newcomer of the topological insulator family. For the AB stacking-bilayer which is lack of the inversion symmetry, it is always topologically trivial, but exhibits an unusual quantum Hall phase with four degenerate low-energy states localized at a single edge. It is suggested that these theoretical findings could be verified experimentally in the transport properties of boron-nitride bylayers. This research was supported by the NSFC (Nos. 60876065, 11074108), PAPD, and NBRPC (Nos. 2009CB929504, 2011CB922102).

Dirac semimetals host three-dimensional (3D) Dirac fermion states in the bulk of crystalline solids, which can be viewed as 3D analogs of graphene. Owing to their relativistic spectrum and unique topological character, these materials hold great promise for fundamental-physics exploration and practical applications. Particularly, they are expected to be ideal parent compounds for engineering various other topological states of matter. In this report, we investigate the possibility to induce and control the topological quantum spin Hall phase in a Dirac semimetal thin film by using a vertical electric field. We show that through the interplay between the quantum confinement effect and the field-induced coupling between sub-bands, the sub-band gap can be tuned and inverted. During this process, the system undergoes a topological phase transition between a trivial band insulator and a quantum spin Hall insulator. Consequently, one can switch the topological edge channels on and off by purely electrical means, making the system a promising platform for constructing topological field effect transistors. PMID:26420343

While two-dimensional (2D) topological insulators (TI's) initiated the field of topological materials, only very few materials were discovered to date and the direct access to their quantum spin Hall edge states has been challenging due to material issues. Here, we introduce a new 2D TI material, Sb few layer films. Electronic structures of ultrathin Sb islands grown on Bi2Te2Se are investigated by scanning tunneling microscopy. The maps of local density of states clearly identify robust edge electronic states over the thickness of three bilayers in clear contrast to thinner islands. This indicates that topological edge states emerge through a 2D topological phase transition predicted between three and four bilayer films in recent theory. The non-trivial phase transition and edge states are confirmed for epitaxial films by extensive density-functional-theory calculations. This work provides an important material platform to exploit microscopic aspects of the quantum spin Hall phase and its quantum phase transition. PMID:27624972

The role of topological point defects (hedgehogs) in the phase transition of the classical Heisenberg model in three dimensions is investigated by using Monte Carlo simulations. Simulations of the behavior of the defects near the phase transition show that the number density of defects increases sharply and defect pairs with separations comparable to the sample size begin to appear as the temperature is increased through the transition temperature. In simulations in a restricted ensemble in which spin configurations containing defects are not allowed, the system appears to remain ordered at all temperatures. Simulations in which the spin-spin interaction is set equal to zero and the number density of defects is controlled by varying a 'chemical potential' term indicate that the system is ordered if the number density of defect pairs is sufficiently small. These results show that topological defects play a crucial role in the three-dimensional Heisenberg transition in the sense that configurations containing defect pairs are necessary for the transition from the ferromagnetic to paramagnetic phase to occur. Such a conclusion is also consistent with a Renormalization Group study of the O(n) model, which suggests that topological defects should be explicitly taken into account for a correct description of the critical behavior in models including the three-dimensional Heisenberg model.

For a gapped disordered many-body system with both internal and translation symmetry, one can define the corresponding weak and strong symmetry protected topological (SPT) phases. A strong SPT phase is protected by the internal symmetry G only while a weak SPT phase, fabricated by alignment of a strong SPT state in a lower dimension, requires additional discrete translation symmetry protection. In this paper, we construct a phase transition between weak and strong SPT phase in a strongly interacting boson system. The starting point of our construction is the superconducting Dirac fermions with pair density wave (PDW) order in 2 d . We first demonstrate that the nodal line of the PDW contains a 1 d boson SPT phase. We further show that melting the PDW stripe and condensing the nodal line provoke the transition from weak to strong SPT phase in 2 d . The phase transition theory contains an O(4) nonlinear-σ model (NL σ M ) with topological Θ term emerging from the proliferation of domain walls bound to an SPT chain. A similar scheme also applies to weak-strong SPT transition in other dimensions and predicts possible phase transition from 2 d to 3 d topological order.

Inelastic scattering off magnetic impurities in a spin-chiral two-dimensional electron gas, e.g., the Rashba system, is shown to generate topological changes in the spin texture of the electron waves emanating from the scattering center. While elastic scattering gives rise to a purely in-plane spin texture for an in-plane magnetic scattering potential, out-of-plane components emerge upon activation of inelastic scattering processes. This property leads to a possibility to make controlled transitions between trivial and nontrivial topologies of the spin texture.

We report on terahertz photoconductivity under magnetic field up to 16 T of field effect transistor based on HgTe quantum well (QW) with an inverted band structure. We observe pronounced cyclotron resonance and Shubnikov-de Haas-like oscillations, indicating a high mobility electron gas in the transistor channel. We discover that nonlinearity of the transistor channel allows for observation of characteristic features in photoconductivity at critical magnetic field corresponding to the phase transition between topological quantum spin Hall and trivial quantum Hall states in HgTe QW. Our results pave the way towards terahertz topological field effect transistors.

Recent experiments by Sengupta et al. (Phys. Rev. Lett. 2013) revealed interesting transitions that can occur in flow of nematic liquid crystal under carefully controlled conditions within a long microfluidic channel of rectangular cross-section, with homeotropic anchoring at the walls. At low flow rates the director field of the nematic adopts a configuration that is dominated by the surface anchoring, being nearly parallel to the channel height direction over most of the cross-section; but at high flow rates there is a transition to a flow-dominated state, where the director configuration at the channel centerline is aligned with the flow (perpendicular to the channel height direction). We analyze simple channel-flow solutions to the Leslie-Ericksen model for nematics. We demonstrate that two solutions exist, at all flow rates, but that there is a transition between the elastic free energies of these solutions: the anchoring-dominated solution has the lowest energy at low flow rates, and the flow-dominated solution has lowest energy at high flow rates. NSF DMS 1211713.

We investigate the topological phase transition on interacting square lattices via the non-Abelian potential by employing the real-space cellular dynamical mean-field theory combining with the continuous-time Monte Carlo method. For a weak on-site Hubbard interaction, a topological band insulating state with a pair of gapless edge states is induced by a next-nearest-neighbor hopping. A phase transition from the metallic phase to the Mott insulating phase is observed when the interaction is increased. These two phases can be distinguished by detecting whether a bulk gap in the K-dependent spectral function exists. The whole phase diagrams as functions of the interaction, next-nearest-neighbor hopping energy, and temperature are presented. The experimental setup to observe these new interesting phase transitions is also discussed.

We study the formation of transportation networks of the true slime mold Physarum polycephalum after fragmentation by shear. Small fragments, called microplasmodia, fuse to form macroplasmodia in a percolation transition. At this topological phase transition, one single giant component forms, connecting most of the previously isolated microplasmodia. Employing the configuration model of graph theory for small link degree, we have found analytically an exact solution for the phase transition. It is generally applicable to percolation as seen, e.g., in vascular networks. PMID:23006405

Topological insulators first observed in electronic systems have inspired many analogues in photonic and phononic crystals in which remarkable one-way propagation edge states are supported by topologically nontrivial band gaps. Such band gaps can be achieved by breaking the time-reversal symmetry to lift the degeneracy associated with Dirac cones at the corners of the Brillouin zone. Here, we report on our construction of a phononic crystal exhibiting a Dirac-like cone in the Brillouin zone center. We demonstrate that simultaneously breaking the time-reversal symmetry and altering the geometric size of the unit cell result in a topologicaltransition that we verify by the Chern number calculation and edge-mode analysis. We develop a complete model based on the tight binding to uncover the physical mechanisms of the topologicaltransition. Both the model and numerical simulations show that the topology of the band gap is tunable by varying both the velocity field and the geometric size; such tunability may dramatically enrich the design and use of acoustic topological insulators.

The postperovskite (ppv) phase transition occurs in the deep mantle close to the core–mantle boundary (CMB). For this reason, we must include in the dynamical considerations both the Clapeyron slope and the temperature intercept, Tint, which is the temperature of the phase transition at the CMB pressure. For a CMB temperature greater than Tint, there is a double crossing of the phase boundary by the geotherms associated with the descending flow. We have found a great sensitivity of the shape of the ppv surface due to the CMB from variations of various parameters such as the amount of internal heating, the Clapeyron slope, and the temperature intercept. Three-dimensional spherical models of mantle convection that can satisfy the seismological constraints depend on the Clapeyron slope. At moderate value, 8 MPa/K, the best fit is found with a core heat flow amounting for 40% of the total heat budget (≈15 TW), whereas for 10 MPa/K the agreement is for a lower core heat flow (20%, ≈7.5 TW). In all cases, these solutions correspond to a temperature intercept 200 K lower than the CMB temperature. These models have holes of perovskite adjacent to ppv in regions of hot upwellings. PMID:17483485

Spin- and angle-resolved photoemission spectroscopy measurements were performed on Bi1-xSbx samples at x=0.04, 0.07, and 0.21 to study the change of the surface band structure from nontopological to topological. Energy shift of the T and Ls bulk bands with Sb concentration is quantitatively evaluated. An edge state becomes topologically nontrivial at x=0.04. An additional trivial edge state appears at the L band gap that forms at x>0.04 and apparently hybridize with the nontrivial edge state. A scenario for the topologicaltransition mechanism is presented. Related issues of self-energy and temperature dependence of the surface state are also considered.

We consider a class of quantum Hall topological insulators: topologically nontrivial states with zero Chern number at finite magnetic field, in which the counterpropagating edge states are protected by a symmetry (spatial or spin) other than time-reversal. HgTe-type heterostructures and graphene are among the relevant systems. We study the effect of electron interactions on the topological properties of the system. We particularly focus on the vicinity of the topological phase transition, marked by the crossing of two Landau levels, where the system is a strongly interacting quantum Hall ferromagnet. We analyze the edge properties using the formalism of the nonlinear σ -model. We establish the symmetry requirement for the topological protection in this interacting system: effective continuous U(1) symmetry with respect to uniaxial isospin rotations must be preserved. If U(1) symmetry is preserved, the topologically nontrivial phase persists; its edge is a helical Luttinger liquid with highly tunable effective interactions. We obtain explicit analytical expressions for the parameters of the Luttinger liquid in the quantum-Hall-ferromagnet regime. However, U(1) symmetry may be broken, either spontaneously or by U(1)-asymmetric interactions. In either case, interaction-induced transitions occur to the respective topologically trivial phases with gapped edge charge excitations.

In this paper, we take into account black hole solutions of Brans-Dicke-Maxwell theory and investigate their stability and phase transition points. We apply the concept of geometry in thermodynamics to obtain phase transition points and compare its results with those, calculated in the canonical ensemble through heat capacity. We show that these black holes enjoy second order phase transitions. We also show that there is a lower bound for the horizon radius of physical charged black holes in Brans-Dicke theory, which originates from restrictions of positivity of temperature. In addition, we find that employing a specific thermodynamical metric in the context of geometrical thermodynamics yields divergencies for the thermodynamical Ricci scalar in places of the phase transitions. It will be pointed out that due to the characteristic behavior of the thermodynamical Ricci scalar around its divergence points, one is able to distinguish the physical limitation point from the phase transitions. In addition, the free energy of these black holes will be obtained and its behavior will be investigated. It will be shown that the behavior of the free energy in the place where the heat capacity diverges demonstrates second order phase transition characteristics.

Transport networks are found at the heart of myriad natural systems, yet are poorly understood, except for the case of river networks. The Scheidegger model, in which rivers are convergent random walks, has been studied only in the case of flat topography, ignoring the variety of curved geometries found in nature. Embedding this model on a cone, we find a convergent and a divergent phase, corresponding to few, long basins and many, short basins, respectively, separated by a singularity, indicating a phase transition. Quantifying basin shape using Hacks law l˜ah gives distinct values for h, providing a method of testing our hypotheses. The generality of our model suggests implications for vascular morphology, in particular, differing number and shapes of arterial and venous trees.

Recently I proposed a simple dynamical network model for discrete space-time that self-organizes as a graph with Hausdorff dimension d(H)=4. The model has a geometric quantum phase transition with disorder parameter (d(H)-d(s)), where d(s) is the spectral dimension of the dynamical graph. Self-organization in this network model is based on a competition between a ferromagnetic Ising model for vertices and an antiferromagnetic Ising model for edges. In this paper I solve a toy version of this model defined on a bipartite graph in the mean-field approximation. I show that the geometric phase transition corresponds exactly to the antiferromagnetic transition for edges, the dimensional disorder parameter of the former being mapped to the staggered magnetization order parameter of the latter. The model has a critical point with long-range correlations between edges, where a continuum random geometry can be defined, exactly as in Kazakov's famed 2D random lattice Ising model but now in any number of dimensions. PMID:26764755

Recently I proposed a simple dynamical network model for discrete space-time that self-organizes as a graph with Hausdorff dimension dH=4 . The model has a geometric quantum phase transition with disorder parameter (dH-ds) , where ds is the spectral dimension of the dynamical graph. Self-organization in this network model is based on a competition between a ferromagnetic Ising model for vertices and an antiferromagnetic Ising model for edges. In this paper I solve a toy version of this model defined on a bipartite graph in the mean-field approximation. I show that the geometric phase transition corresponds exactly to the antiferromagnetic transition for edges, the dimensional disorder parameter of the former being mapped to the staggered magnetization order parameter of the latter. The model has a critical point with long-range correlations between edges, where a continuum random geometry can be defined, exactly as in Kazakov's famed 2D random lattice Ising model but now in any number of dimensions.

Quantum spin Hall (QSH) insulators exhibit a bulk insulting gap and metallic edge states characterized by nontrivial topology. Here, we used first-principles calculations to investigate the electronic and topological properties of halogenated silicon germanide (X2-SiGe, with X = F, Cl, and Br) monolayers, which we found to be trivial semiconductors with energy band gaps ranging from 500 meV to 900 meV. Interestingly, we found that under 8% strain, X2-SiGe monolayers behave as QSH insulators with global band gaps between 53 meV and 123 meV. The underlying mechanism of the topological phase transition is the strain-induced s-p band inversion. The nontrivial topological features for the strained X2-SiGe monolayers were further confirmed by the presence of topologically protected edge states that form a single Dirac cone in the middle of the bulk band gaps. Therefore, our results reveal that this new family of QSH insulators is promising for room temperature applications in spintronics and quantum computation devices. PMID:26758453

We propose a method to associate a differentiable Riemannian manifold to a generic many-degrees-of-freedom discrete system which is not described by a Hamiltonian function. Then, in analogy with classical statistical mechanics, we introduce an entropy as the logarithm of the volume of the manifold. The geometric entropy so defined is able to detect a paradigmatic phase transition occurring in random graphs theory: the appearance of the “giant component” according to the Erdös-Rényi theorem.

We report on a temperature-induced transition from a conventional semiconductor to a two-dimensional topological insulator investigated by means of magnetotransport experiments on HgTe/CdTe quantum well structures. At low temperatures, we are in the regime of the quantum spin Hall effect and observe an ambipolar quantized Hall resistance by tuning the Fermi energy through the bulk band gap. At room temperature, we find electron and hole conduction that can be described by a classical two-carrier model. Above the onset of quantized magnetotransport at low temperature, we observe a pronounced linear magnetoresistance that develops from a classical quadratic low-field magnetoresistance if electrons and holes coexist. Temperature-dependent bulk band structure calculations predict a transition from a conventional semiconductor to a topological insulator in the regime where the linear magnetoresistance occurs.

The mechanism for the fast switching between amorphous, metastable, and crystalline structures in chalcogenide phase-change materials has been a long-standing puzzle. Based on first-principles calculations, we study the atomic and electronic properties of metastable Ge{sub 2}Sb{sub 2}Te{sub 5} and investigate the atomic disorder to understand the transition between crystalline hexagonal and cubic structures. In addition, we study the topological insulating property embedded in these compounds and its evolution upon structural changes and atomic disorder. We also discuss the role of the surface-like states arising from the topological insulating property in the metal-insulator transition observed in the hexagonal structure.

We present first-principles calculations of electronic structures of a class of two-dimensional (2D) honeycomb structures of group-V binary compounds. Our results show these new 2D materials are stable semiconductors with direct or indirect band gaps. The band gap can be tuned by applying lattice strain. During their stretchable regime, they all exhibit metal-indirect gap semiconductor-direct gap semiconductor-topological insulator (TI) transitions with increasing strain from negative (compressive) to positive (tensile) values. The topological phase transition results from the band inversion at the Γ point which is due to the evolution of bonding and anti-bonding states under lattice strain. PMID:26656257

We extend the non-Hermitian one-dimensional quantum walk model [Phys. Rev. Lett. 102, 065703 (2009), 10.1103/PhysRevLett.102.065703] by taking the dephasing effect into account. We prove that the feature of topologicaltransition does not change even when dephasing between the sites within units is present. The potential experimental observation of our theoretical results in the circuit QED system consisting of superconducting qubit coupled to a superconducting resonator mode is discussed and numerically simulated. The results clearly show a topologicaltransition in quantum walk and display the robustness of such a system to the decay and dephasing of qubits. We also discuss how to extend this model to higher dimension in the circuit QED system.

We study the mean-field BCS-BEC evolution of a uniform Fermi gas on a single-band triangular lattice and construct its ground-state phase diagrams, showing a wealth of topological quantum phase transitions between gapped and gapless superfluids that are induced by the interplay of an out-of-plane Zeeman field and a generic non-Abelian gauge field.

We present a density functional theory study on the thermal bistability of a number of photochromic diarylethenes, with emphasis on the free energy barrier of the ground-state ring-opening process. We found that the free energy barrier is correlated with the geometrical and vibrational character of the transition state, in particular the distance between the two reactive carbon atoms, the out-of-plane angles of the methyl groups at the reactive carbon atoms, and the imaginary vibrational frequency. Based on these relationships we propose a linear fitting expression for the free energy barrier in terms of the three aforementioned transition-state quantities and obtained a correlation coefficient of R(2) = 0.971. In this way quantum chemical calculations may provide insight and structure-property relationships, which can be applied in the development of novel photochromic materials. PMID:26267793

We identify two distinct scaling regimes in the frequency-magnitude distribution of global earthquakes. Specifically, we measure the scaling exponent b = 1.0 for "small" earthquakes with 5.5 < m < 7.6 and b = 1.5 for "large" earthquakes with 7.6 < m < 9.0. This transition at mt = 7.6, can be explained by geometric constraints on the rupture. In conjunction with supporting literature, this corroborates theories in favor of fully self-similar and magnitude independent earthquake physics. We also show that the scaling behavior and abrupt transition between the scaling regimes imply that earthquake ruptures have compact shapes and smooth rupture-fronts.

We use molecular dynamics simulations to investigate dynamic heterogeneities and the potential energy landscape of the Gaussian core model (GCM). Despite the nearly Gaussian statistics of particles' displacements, the GCM exhibits giant dynamic heterogeneities close to the dynamic transition temperature. The divergence of the four-point susceptibility is quantitatively well described by the inhomogeneous version of the mode-coupling theory. Furthermore, the potential energy landscape of the GCM is characterized by large energy barriers, as expected from the lack of activated, hopping dynamics, and display features compatible with a geometrictransition. These observations demonstrate that all major features of mean-field dynamic criticality can be observed in a physically sound, three-dimensional model.

We use molecular dynamics simulations to investigate dynamic heterogeneities and the potential energy landscape of the Gaussian core model (GCM). Despite the nearly Gaussian statistics of particles' displacements, the GCM exhibits giant dynamic heterogeneities close to the dynamic transition temperature. The divergence of the four-point susceptibility is quantitatively well described by the inhomogeneous version of the mode-coupling theory. Furthermore, the potential energy landscape of the GCM is characterized by large energy barriers, as expected from the lack of activated, hopping dynamics, and display features compatible with a geometrictransition. These observations demonstrate that all major features of mean-field dynamic criticality can be observed in a physically sound, three-dimensional model. PMID:27176347

Low-buckled silicene is a prototypical quantum spin Hall insulator with the topological quantum phase transition controlled by an out-of-plane electric field. We show that this field-induced electronic transition can be further tuned by an in-plane biaxial strain ε, owing to the curvature-dependent spin-orbit coupling (SOC): There is a Z{sub 2} = 1 topological insulator phase for biaxial strain |ε| smaller than 0.07, and the band gap can be tuned from 0.7 meV for ε=+0.07 up to 3.0 meV for ε=−0.07. First-principles calculations also show that the critical field strength E{sub c} can be tuned by more than 113%, with the absolute values nearly 10 times stronger than the theoretical predictions based on a tight-binding model. The buckling structure of the honeycomb lattice thus enhances the tunability of both the quantum phase transition and the SOC-induced band gap, which are crucial for the design of topological field-effect transistors based on two-dimensional materials.

Discovery of two-dimensional (2D) topological insulator such as group-V films initiates challenges in exploring exotic quantum states in low dimensions. Here, we perform first-principles calculations to study the geometric and electronic properties in 2D arsenene monolayer with hydrogenation (HAsH). We predict a new σ-type Dirac cone related to the px,y orbitals of As atoms in HAsH, dependent on in-plane tensile strain. Noticeably, the spin-orbit coupling (SOC) opens a quantum spin Hall (QSH) gap of 193 meV at the Dirac cone. A single pair of topologically protected helical edge states is established for the edges, and its QSH phase is confirmed with topological invariant Z2 = 1. We also propose a 2D quantum well (QW) encapsulating HAsH with the h-BN sheet on each side, which harbors a nontrivial QSH state with the Dirac cone lying within the band gap of cladding BN substrate. These findings provide a promising innovative platform for QSH device design and fabrication operating at room temperature. PMID:26839209

Discovery of two-dimensional (2D) topological insulator such as group-V films initiates challenges in exploring exotic quantum states in low dimensions. Here, we perform first-principles calculations to study the geometric and electronic properties in 2D arsenene monolayer with hydrogenation (HAsH). We predict a new σ-type Dirac cone related to the px,y orbitals of As atoms in HAsH, dependent on in-plane tensile strain. Noticeably, the spin-orbit coupling (SOC) opens a quantum spin Hall (QSH) gap of 193 meV at the Dirac cone. A single pair of topologically protected helical edge states is established for the edges, and its QSH phase is confirmed with topological invariant Z2 = 1. We also propose a 2D quantum well (QW) encapsulating HAsH with the h-BN sheet on each side, which harbors a nontrivial QSH state with the Dirac cone lying within the band gap of cladding BN substrate. These findings provide a promising innovative platform for QSH device design and fabrication operating at room temperature.

Discovery of two-dimensional (2D) topological insulator such as group-V films initiates challenges in exploring exotic quantum states in low dimensions. Here, we perform first-principles calculations to study the geometric and electronic properties in 2D arsenene monolayer with hydrogenation (HAsH). We predict a new σ-type Dirac cone related to the px,y orbitals of As atoms in HAsH, dependent on in-plane tensile strain. Noticeably, the spin-orbit coupling (SOC) opens a quantum spin Hall (QSH) gap of 193 meV at the Dirac cone. A single pair of topologically protected helical edge states is established for the edges, and its QSH phase is confirmed with topological invariant Z2 = 1. We also propose a 2D quantum well (QW) encapsulating HAsH with the h-BN sheet on each side, which harbors a nontrivial QSH state with the Dirac cone lying within the band gap of cladding BN substrate. These findings provide a promising innovative platform for QSH device design and fabrication operating at room temperature. PMID:26839209

A measure of cluster size heterogeneity (H), introduced by Lee et al. [Phys. Rev. E 84, 020101 (2011)] in the context of explosive percolation, was recently applied to random percolation and to domains of parallel spins in the Ising and Potts models. It is defined as the average number of different domain sizes in a given configuration and a new exponent was introduced to explain its scaling with the size of the system. In thermal spin models, however, physical clusters take into account the temperature-dependent correlation between neighboring spins and encode the critical properties of the phase transition. We here extend the measure of H to these clusters and, moreover, present new results for the geometric domains for both d=2 and 3. We show that the heterogeneity associated with geometric domains has a previously unnoticed double peak, thus being able to detect both the thermal and percolative transitions. An alternative interpretation for the scaling of H that does not introduce a new exponent is also proposed. PMID:25974445

A measure of cluster size heterogeneity (H ), introduced by Lee et al. [Phys. Rev. E 84, 020101 (2011), 10.1103/PhysRevE.84.020101] in the context of explosive percolation, was recently applied to random percolation and to domains of parallel spins in the Ising and Potts models. It is defined as the average number of different domain sizes in a given configuration and a new exponent was introduced to explain its scaling with the size of the system. In thermal spin models, however, physical clusters take into account the temperature-dependent correlation between neighboring spins and encode the critical properties of the phase transition. We here extend the measure of H to these clusters and, moreover, present new results for the geometric domains for both d =2 and 3. We show that the heterogeneity associated with geometric domains has a previously unnoticed double peak, thus being able to detect both the thermal and percolative transitions. An alternative interpretation for the scaling of H that does not introduce a new exponent is also proposed.

Three-dimensional Dirac semimetals (DSMs) are materials that have massless Dirac electrons and exhibit exotic physical properties. It has been suggested that structurally distorting a DSM can create a topological insulator but this has not yet been experimentally verified. Furthermore, Majorana fermions have been theoretically proposed to exist in materials that exhibit both superconductivity and topological surface states. Here we show that the cubic Laves phase Au2Pb has a bulk Dirac cone that is predicted to gap on cooling through a structural phase transition at 100 K. The low temperature phase can be assigned a Z2=-1 topological index, and this phase becomes superconducting below 1.2 K. These characteristics make Au2Pb a unique platform for studying the transition between bulk Dirac electrons and topological surface states as well as studying the interaction of superconductivity with topological surface states, combining many different properties of emergent materials—superconductivity, bulk Dirac electrons, and a topologically nontrivial Z2 invariant.

The role of topological point defects (hedgehogs) in the phase transition of the classical Heisenberg model in three dimensions is investigated by using Monte Carlo simulations. Simulations of the behavior of the defects near the phase transition show that the number density of defects increases sharply and defect pairs with separations comparable to the sample size begin to appear as the temperature is increased through the transition temperature. In simulations in a restricted ensemble in which spin configurations containing defects are not allowed, the system appears to remain ordered at all temperatures. Simulations in which the spin-spin interaction is set equal to zero and the number density of defects is controlled by varying a ``chemical potential'' term indicate that the system is ordered if the number density of defect pairs is sufficiently small. These results show that topological defects play a crucial role in the three-dimensional Heisenberg transition in the sense that configurations containing defect pairs are necessary for the transition from the ferromagnetic to the paramagnetic phase to occur.

We study charged, static, topological black holes in pure Gauss-Bonnet gravity in asymptotically AdS space. As in general relativity, the theory possesses a unique nondegenerate AdS vacuum. It also admits charged black hole solutions which asymptotically behave as the Reissner-Nordström AdS black hole. We discuss black hole thermodynamics of these black holes. Then we study phase transitions in a dual quantum field theory in four dimensions, with the Stückelberg scalar field as an order parameter. We find in the probe limit that the black hole can develop hair below some critical temperature, which suggests a phase transition. Depending on the scalar coupling constants, the phase transition can be first or second order. Analysis of the free energy reveals that, comparing the two solutions, the hairy state is energetically favorable, thus a phase transition will occur in a dual field theory.

A 3D Topological Insulator (TI) is an intrinsically stratified electronic material characterized by an insulating bulk and Dirac free electrons at the interface with vacuum or another dielectric. In this paper, we investigate, through terahertz (THz) spectroscopy, the plasmon excitation of Dirac electrons on thin films of (Bi1-xInx)2Se3 TI patterned in the form of a micro-ribbon array, across a Quantum Phase Transition (QPT) from the topological to a trivial insulating phase. The latter is achieved by In doping onto the Bi-site and is characterized by massive electrons at the surface. While the plasmon frequency is nearly independent of In content, the plasmon width undergoes a sudden broadening across the QPT, perfectly mirroring the single particle (free electron) behavior as measured on the same films. This strongly suggests that the topological protection from backscattering characterizing Dirac electrons in the topological phase extends also to their plasmon excitations. PMID:26852877

A 3D Topological Insulator (TI) is an intrinsically stratified electronic material characterized by an insulating bulk and Dirac free electrons at the interface with vacuum or another dielectric. In this paper, we investigate, through terahertz (THz) spectroscopy, the plasmon excitation of Dirac electrons on thin films of (Bi1-xInx)2Se3 TI patterned in the form of a micro-ribbon array, across a Quantum Phase Transition (QPT) from the topological to a trivial insulating phase. The latter is achieved by In doping onto the Bi-site and is characterized by massive electrons at the surface. While the plasmon frequency is nearly independent of In content, the plasmon width undergoes a sudden broadening across the QPT, perfectly mirroring the single particle (free electron) behavior as measured on the same films. This strongly suggests that the topological protection from backscattering characterizing Dirac electrons in the topological phase extends also to their plasmon excitations.A 3D Topological Insulator (TI) is an intrinsically stratified electronic material characterized by an insulating bulk and Dirac free electrons at the interface with vacuum or another dielectric. In this paper, we investigate, through terahertz (THz) spectroscopy, the plasmon excitation of Dirac electrons on thin films of (Bi1-xInx)2Se3 TI patterned in the form of a micro-ribbon array, across a Quantum Phase Transition (QPT) from the topological to a trivial insulating phase. The latter is achieved by In doping onto the Bi-site and is characterized by massive electrons at the surface. While the plasmon frequency is nearly independent of In content, the plasmon width undergoes a sudden broadening across the QPT, perfectly mirroring the single particle (free electron) behavior as measured on the same films. This strongly suggests that the topological protection from backscattering characterizing Dirac electrons in the topological phase extends also to their plasmon excitations. Electronic

There are many interests to achieve long-range magnetic order in topological insulators of Bi2Se3 or Bi2Te3 by doping magnetic transition metals such as Fe and Mn. The transition metals act as not only magnetic dopants but also electric dopants because they are usually divalent. However, if the doping elements are rare-earth metals such as Gd, which are trivalent, only magnetic moments can be introduced. We fabricated single crystals of Bi2-xGdxTe3 (0 ≤ × ≤ 0.2), in which we observed magnetic phase change from paramagnetic (PM) to antiferromagnetic (AFM) phase by increasing x. This PM-to-AFM phase transition agrees with the density functional theory calculations showing a weak and short-ranged Gd-Gd AFM coupling via the intervening Te ions. The critical point corresponding to the magnetic phase transition is x = 0.09, where large linear magnetoresistance and highly anisotropic Shubnikov-de Haas oscillations are observed. These results are discussed with two-dimensional properties of topological surface state electrons. PMID:25974047

There are many interests to achieve long-range magnetic order in topological insulators of Bi2Se3 or Bi2Te3 by doping magnetic transition metals such as Fe and Mn. The transition metals act as not only magnetic dopants but also electric dopants because they are usually divalent. However, if the doping elements are rare-earth metals such as Gd, which are trivalent, only magnetic moments can be introduced. We fabricated single crystals of Bi2-xGdxTe3 (0 ≤ × ≤ 0.2), in which we observed magnetic phase change from paramagnetic (PM) to antiferromagnetic (AFM) phase by increasing x. This PM-to-AFM phase transition agrees with the density functional theory calculations showing a weak and short-ranged Gd-Gd AFM coupling via the intervening Te ions. The critical point corresponding to the magnetic phase transition is x = 0.09, where large linear magnetoresistance and highly anisotropic Shubnikov-de Haas oscillations are observed. These results are discussed with two-dimensional properties of topological surface state electrons. PMID:25974047

In studying the dynamics of large N{sub c}, SU(N{sub c}) gauge theory at finite temperature with fundamental quark flavors in the quenched approximation, we observe a first order phase transition. A quark condensate forms at finite quark mass, and the value of the condensate varies smoothly with the quark mass for generic regions in parameter space. At a particular value of the quark mass, there is a finite discontinuity in the condensate's vacuum expectation value, corresponding to a first order phase transition. We study the gauge theory via its string dual formulation using the AdS/CFT conjecture, the string dual being the near-horizon geometry of N{sub c} D3-branes at finite temperature, AdS{sub 5}-SchwarzschildxS{sup 5}, probed by a D7-brane. The D7-brane has topology R{sup 4}xS{sup 3}xS{sup 1} and allowed solutions correspond to either the S{sup 3} or the S{sup 1} shrinking away in the interior of the geometry. The phase transition represents a jump between branches of solutions having these two distinct D-brane topologies. The transition also appears in the meson spectrum.

We theoretically study the dynamics of topological phase transition in one-dimensional (1D) spin-orbit coupled (SOC) Fermi gases with attractive interaction as a means of detecting the phase transition. The transition from conventional (trivial) superfluid to topological superfluid phase happens as the intensity of the Raman lasers (Zeeman field) is ramped above the critical value. To minimize effect of heating, we propose to ramp from a conventional superfluid phase through the topological phase transition and back. We calculate the momentum distribution of the atoms after the ramp by solving the time-dependent Bogoliubov-de Gennes (BdG) equations self-consistently with the initial state of the Fermi gas being the thermal state. We show that the phase transition can be detected by measuring the scaling of the momentum distribution with the ramp rate. This work is supported by NSF-JQI-PFC and ARO-Atomtronics-MURI.

Single layered transition metal dichalcogenides have attracted tremendous research interest due to their structural phase diversities. By using a global optimization approach, we have discovered a new phase of transition metal dichalcogenides (labelled as T''), which is confirmed to be energetically, dynamically and kinetically stable by our first-principles calculations. The new T'' MoS2 phase exhibits an intrinsic quantum spin Hall (QSH) effect with a nontrivial gap as large as 0.42 eV, suggesting that a two-dimensional (2D) topological insulator can be achieved at room temperature. Most interestingly, there is a topological phase transition simply driven by a small tensile strain of up to 2%. Furthermore, all the known MX2 (M = Mo or W; X = S, Se or Te) monolayers in the new T'' phase unambiguously display similar band topologies and strain controlled topological phase transitions. Our findings greatly enrich the 2D families of transition metal dichalcogenides and offer a feasible way to control the electronic states of 2D topological insulators for the fabrication of high-speed spintronics devices.Single layered transition metal dichalcogenides have attracted tremendous research interest due to their structural phase diversities. By using a global optimization approach, we have discovered a new phase of transition metal dichalcogenides (labelled as T''), which is confirmed to be energetically, dynamically and kinetically stable by our first-principles calculations. The new T'' MoS2 phase exhibits an intrinsic quantum spin Hall (QSH) effect with a nontrivial gap as large as 0.42 eV, suggesting that a two-dimensional (2D) topological insulator can be achieved at room temperature. Most interestingly, there is a topological phase transition simply driven by a small tensile strain of up to 2%. Furthermore, all the known MX2 (M = Mo or W; X = S, Se or Te) monolayers in the new T'' phase unambiguously display similar band topologies and strain controlled topological

We numerically study the quantum phase transitions and the stability of Majorana zero modes in a generalized Kitaev model in one dimension when the chemical potential is periodically modulating in space. By using the exact diagonalization method for open boundary condition, we investigate the ground-state phases in terms of the non-local properties such as the entanglement spectrum (ES) and the string correlation functions. When we vary the phase of the modulation, the number of the Majorana zero modes changes, which manifests itself in the degeneracy of the lowest level of the ES. Next, we study the quantum phase transitions driven by the change in the amplitude of the modulation. In particular, for certain values of the wave number and the phase of the modulation, we observe a quantum phase transition from one topological phase into another where the string correlation function oscillates in space. We also show a case where the degeneracy of the ES does not change even for large enough amplitude of the modulation. Finally, we characterize the phases of the system with periodic boundary condition by the topological invariant, which reflects the number of the zero-energy excitations.

We illustrate how geometric gauge forces and topological phase effects emerge in atomic and molecular systems without employing assumptions that rely on adiabaticity. We show how geometric magnetism may be harnessed to engineer novel quantum devices including a velocity sieve, a component in mass spectrometers, for neutral atoms. We introduce and outline a possible experimental setup that demonstrates topological interferometry for neutral spin-1/2 systems. For that two-level system, we study the transition from Abelian to non-Abelian behavior and explore its relation to the molecular Aharonov-Bohm effect.

High-pressure Raman spectroscopy and x-ray diffraction of Sb2S3 up to 53 GPa reveals two phase transitions at 5 GPa and 15 GPa. The first transition is evidenced by noticeable compressibility changes in distinct Raman-active modes, in the lattice parameter axial ratios, the unit cell volume, as well as in specific interatomic bond lengths and bond angles. By taking into account relevant results from the literature, we assign these effects to a second-order isostructural transition arising from an electronic topologicaltransition in Sb2S3 near 5 GPa. Close comparison between Sb2S3 and Sb2Se3 up to 10 GPa reveals a slightly diverse structural behavior for these two compounds after the isostructural transition pressure. This structural diversity appears to account for the different pressure-induced electronic behavior of Sb2S3 and Sb2Se3 up to 10 GPa, i.e. the absence of an insulator-metal transition in Sb2S3 up to that pressure. Finally, the second high-pressure modification appearing above 15 GPa appears to trigger a structural disorder at ~20 GPa full decompression from 53 GPa leads to the recovery of an amorphous state.

High-pressure Raman spectroscopy and x-ray diffraction of Sb2S3 up to 53 GPa reveals two phase transitions at 5 GPa and 15 GPa. The first transition is evidenced by noticeable compressibility changes in distinct Raman-active modes, in the lattice parameter axial ratios, the unit cell volume, as well as in specific interatomic bond lengths and bond angles. By taking into account relevant results from the literature, we assign these effects to a second-order isostructural transition arising from an electronic topologicaltransition in Sb2S3 near 5 GPa. Close comparison between Sb2S3 and Sb2S3 up to 10 GPa reveals a slightly diverse structuralmore » behavior for these two compounds after the isostructural transition pressure. This structural diversity appears to account for the different pressure-induced electronic behavior of Sb2S3 and Sb2S3 up to 10 GPa, i.e. the absence of an insulator-metal transition in Sb2S3 up to that pressure. Lastly, the second high-pressure modification appearing above 15 GPa appears to trigger a structural disorder at ~20 GPa; full decompression from 53 GPa leads to the recovery of an amorphous state.« less

High-pressure Raman spectroscopy and x-ray diffraction of Sb2S3 up to 53 GPa reveals two phase transitions at 5 GPa and 15 GPa. The first transition is evidenced by noticeable compressibility changes in distinct Raman-active modes, in the lattice parameter axial ratios, the unit cell volume, as well as in specific interatomic bond lengths and bond angles. By taking into account relevant results from the literature, we assign these effects to a second-order isostructural transition arising from an electronic topologicaltransition in Sb2S3 near 5 GPa. Close comparison between Sb2S3 and Sb2Se3 up to 10 GPa reveals a slightly diverse structural behavior for these two compounds after the isostructural transition pressure. This structural diversity appears to account for the different pressure-induced electronic behavior of Sb2S3 and Sb2Se3 up to 10 GPa, i.e. the absence of an insulator-metal transition in Sb2S3 up to that pressure. Finally, the second high-pressure modification appearing above 15 GPa appears to trigger a structural disorder at ~20 GPa; full decompression from 53 GPa leads to the recovery of an amorphous state. PMID:27048930

(HgTe)N(CdTe)M(110) and (001) superlattices are studied by means of ab initio calculations versus the thickness of the HgTe quantum wells (QWs). The used approximate quasiparticle theory including spin-orbit coupling (SOC) gives the correct band ordering, band gap, and SOC splitting for bulk HgTe and CdTe. The resulting band discontinuities indicate confinement also for occupied states. In agreement with earlier k .p calculations and experiments we find a topologicaltransition from the topological nontrivial quantum spin Hall state into a trivial insulator with decreasing QW thickness. The spatial localization near the interfaces and the spin polarization are demonstrated for the edge states for QWs with thicknesses near the critical one. They do not depend on the QW orientation and are therefore topologically protected. Below the critical QW thickness, the trivial insulator exhibits drastic confinement effects with a significant gap opening. We show that the inclusion of inversion symmetry, the nonaxial rotation symmetry of the QWs, and the real QW barriers lead to some agreement but also significant deviations from the predictions within toy models. The deviations concern the critical thickness, the number and localization of edge states, and the possibility to find QW subbands between edge states.

Monolayers of transition-metal dichalcogenides (TMDs) are two-dimensional materials whose low-energy sector consists of two inequivalent valleys. The valence bands have a large spin splitting due to lack of inversion symmetry and strong spin-orbit coupling. Furthermore the spin is polarized up in one valley and down in the other (in directions perpendicular to the two-dimensional crystal). We focus on lightly hole-doped systems where the Fermi surface consists of two disconnected circles with opposite spins. For both proximity induced and intrinsic local attractive interaction induced superconductivity, a fully gapped intervalley pairing state is favored in this system, which is an equal superposition of the singlet and the m =0 triplet for the lack of centrosymmetry. We show that a ferromagnetically ordered magnetic-adatom chain placed on a monolayer TMD superconductor provides a platform to realize a one-dimensional topological superconducting state characterized by the presence of Majorana zero modes at its ends. We obtain the topological phase diagram and show that the topological superconducting phase is affected not only by the adatom spacing and the direction of the magnetic moment, but also by the orientation of the chain relative to the crystal.

Reflectance confocal microscopy is successfully used in infant skin research. Infant skin structure, function, and composition are undergoing a maturation process. We aimed to uncover how the epidermal architecture and cellular topology change with time. Images were collected from three age groups of healthy infants between one and four years of age and adults. Cell centers were manually identified on the images at the stratum granulosum (SG) and stratum spinosum (SS) levels. Voronoi diagrams were used to calculate geometrical and topological parameters. Infant cell density is higher than that of adults and decreases with age. Projected cell area, cell perimeter, and average distance to the nearest neighbors increase with age but do so distinctly between the two layers. Structural entropy is different between the two strata, but remains constant with time. For all ages and layers, the distribution of the number of nearest neighbors is typical of a cooperator network architecture. The topological analysis provides evidence of the maturation process in infant skin. The differences between infant and adult are more pronounced in the SG than SS, while cell cooperation is evident in all cases of healthy skin examined.

Topological quantum phase transitions are numerically investigated in a spin-1/2 dimerized and frustrated Heisenberg chain by using infinite matrix product state representation with the infinite time evolving block decimation method. Quantum fidelity approach is employed to detect the degenerate ground states and quantum phase transitions. By calculating the long-range string order parameters, we find two topological Haldane phases characterized by two long-range string orders. Also, continuous and discontinuous behaviors of von Neumann entropy show that phase transitions between two topological Haldane phases are topologically continuous and discontinuous quantum phase transitions. For the topologically continuous phase transition, the central charge at the critical point is obtained as c = 1, which means that the topologically continuous quantum phase transition belongs to the Gaussian universality class.

The topological property of SrRu$_2$O$_6$ and isostructural CaOs$_2$O$_6$ under various strain conditions is investigated using density functional theory. Based on an analysis of parity eigenvalues, we anticipate that a three-dimensional strong topological insulating state should be realized when band inversion is induced at the A point in the hexagonal Brillouin zone. For SrRu$_2$O$_6$, such a transition requires rather unrealistic tuning, where only the $c$ axis is reduced while other structural parameters are unchanged. However, given the larger spin-orbit coupling and smaller lattice constants in CaOs$_2$O$_6$, the desired topologicaltransition does occur under uniform compressive strain. Our study paves a waymore » to realize a topological insulating state in a complex oxide, which has not been experimentally demonstrated so far.« less

A frustrated spin-1/2 XXZ zigzag chain relevant to Rb2Cu2Mo3O12 is revisited in the light of symmetry-protected topological (SPT) phases. Using a density-matrix renormalization group method for infinite systems, we identify projective representations for four distinct time-reversal invariant SPT phases; two parity-symmetric dimer phases near the Heisenberg and XX limits and two parity-broken vector-chiral (VC) dimer phases in between. A small bond alternation in the nearest-neighbor ferromagnetic exchange coupling induces a direct SPT transition between the two distinct VC dimer phases. It is also found numerically that two Berezinskii-Kosterlitz-Thouless transitions, which occur from the gapless to the two distinct gapped VC phases in the case of δ =0 , meet each other in the case of δ >0 at a Gaussian criticality of the same Tomonaga-Luttinger parameter value as in the SU(2)-symmetric case.

The electronic structure and phase stability of paramagnetic FeSe is computed by using a combination of ab initio methods for calculating band structure and dynamical mean-field theory. Our results reveal a topological change (Lifshitz transition) of the Fermi surface upon a moderate expansion of the lattice. The Lifshitz transition is accompanied with a sharp increase of the local moments and results in an entire reconstruction of magnetic correlations from the in-plane magnetic wave vector, (π,π) to (π,0). We attribute this behavior to a correlation-induced shift of the van Hove singularity originating from the d(xy) and d(xz)/d(yz) bands at the M point across the Fermi level. We propose that superconductivity is strongly influenced, or even induced, by a van Hove singularity. PMID:26382687

Time-reversal symmetric topological insulator (TI) is a novel state of matter that a bulk-insulating state carries dissipationless spin transport along the surfaces, embedded by the Z2 topological invariant. In the noninteracting limit, this exotic state has been intensively studied and explored with realistic systems, such as HgTe/(Hg, Cd)Te quantum wells. On the other hand, electronic correlation plays a significant role in many solid-state systems, which further influences topological properties and triggers topological phase transitions. Yet an interacting TI is still an elusive subject and most related analyses rely on the mean-field approximation and numerical simulations. Among the approaches, the mean-field approximation fails to predict the topological phase transition, in particular at intermediate interaction strength without spontaneously breaking symmetry. In this paper, we develop an analytical approach based on a combined perturbative and self-consistent mean-field treatment of interactions that is capable of capturing topological phase transitions beyond either method when used independently. As an illustration of the method, we study the effects of short-ranged interactions on the Z2 TI phase, also known as the quantum spin Hall (QSH) phase, in three generalized versions of the Kane-Mele (KM) model at half-filling on the honeycomb lattice. The results are in excellent agreement with quantum Monte Carlo (QMC) calculations on the same model and cannot be reproduced by either a perturbative treatment or a self-consistent mean-field treatment of the interactions. Our analytical approach helps to clarify how the symmetries of the one-body terms of the Hamiltonian determine whether interactions tend to stabilize or destabilize a topological phase. Moreover, our method should be applicable to a wide class of models where topologicaltransitions due to interactions are in principle possible, but are not correctly predicted by either perturbative or self

Recently, Ag2Te was experimentally confirmed to be a 3D topological insulator (TI) at ambient pressure. However, the high-pressure behaviors and properties of Ag2Te were rarely reported. Here, a pressure-induced electronic topologicaltransition (ETT) is firstly found in Ag2Te at 1.8 GPa. Before ETT, the positive pressure coefficient of bulk band-gap, which is firstly found in TIs family, is found by both first-principle calculations and in situ high-pressure resistivity measurements. The electrical resistivity obtained at room temperature shows a maximum at 1.8 GPa, which is nearly 3.3 times to that at ambient pressure. This result indicates that the best bulk insulating character and topological nature in Ag2Te can be obtained at this pressure. Furthermore, the high-pressure structural behavior of Ag2Te has been investigated by in situ high-pressure synchrotron powder X-ray diffraction technique up to 33.0 GPa. The accurate pressure-induced phase transition sequence is firstly determined as P21/c → Cmca → Pnma. It is worth noting that the reported isostructural P21/c phase is not existed, and the reported structure of Cmca phase is corrected by CALYPSO methodology. The second high-pressure structure, a long puzzle to previous reports, is determined as Pnma phase. A pressure-induced metallization in Ag2Te is confirmed by the results of temperature-dependent resistivity measurements. PMID:26419707

We report the pressure-induced topological quantum phase transition of BiTeI single crystals using Shubnikov-de Haas oscillations of bulk Fermi surfaces. The sizes of the inner and the outer FSs of the Rashba-split bands exhibit opposite pressure dependence up to P = 3.35 GPa, indicating pressure-tunable Rashba effect. Above a critical pressure P ~ 2 GPa, the Shubnikov-de Haas frequency for the inner Fermi surface increases unusually with pressure, and the Shubnikov-de Haas oscillations for the outer Fermi surface shows an abrupt phase shift. In comparison with band structure calculations, we find that these unusual behaviors originate from the Fermi surface shape change due to pressure-induced band inversion. These results clearly demonstrate that the topological quantum phase transition is intimately tied to the shape of bulk Fermi surfaces enclosing the time-reversal invariant momenta with band inversion. PMID:26522628

Single layered transition metal dichalcogenides have attracted tremendous research interest due to their structural phase diversities. By using a global optimization approach, we have discovered a new phase of transition metal dichalcogenides (labelled as T''), which is confirmed to be energetically, dynamically and kinetically stable by our first-principles calculations. The new T'' MoS2 phase exhibits an intrinsic quantum spin Hall (QSH) effect with a nontrivial gap as large as 0.42 eV, suggesting that a two-dimensional (2D) topological insulator can be achieved at room temperature. Most interestingly, there is a topological phase transition simply driven by a small tensile strain of up to 2%. Furthermore, all the known MX2 (M = Mo or W; X = S, Se or Te) monolayers in the new T'' phase unambiguously display similar band topologies and strain controlled topological phase transitions. Our findings greatly enrich the 2D families of transition metal dichalcogenides and offer a feasible way to control the electronic states of 2D topological insulators for the fabrication of high-speed spintronics devices. PMID:26620395

Based on first-principles calculations and effective Hamiltonian analysis, we predict a topological phase transition from normal to topological insulators and the opening of a gap without breaking the time-reversal symmetry in TlBi(S1-xSex)2. The transition can be driven by modulating the Se concentration, and the rescaled spin-orbit coupling and lattice parameters are the key ingredients for the transition. For topological surface states, the Dirac cone evolves differently as the explicit breaking of inversion symmetry and the energy band can be opened under asymmetry surface. Our results present theoretical evidence for experimental observations [Xu et al., Science 332, 560 (2011); Sato et al., Nat. Phys. 7, 840 (2011)].

New two-dimensional systems such as the surfaces of topological insulators (TIs) and graphene offer the possibility of experimentally investigating situations considered exotic just a decade ago. These situations include the quantum phase transition of the chiral type in electronic systems with a relativistic spectrum. Phonon-mediated (conventional) pairing in the Dirac semimetal appearing on the surface of a TI causes a transition into a chiral superconducting state, and exciton condensation in these gapless systems has long been envisioned in the physics of narrow-band semiconductors. Starting from the microscopic Dirac Hamiltonian with local attraction or repulsion, the Bardeen-Cooper-Schrieffer type of Gaussian approximation is developed in the framework of functional integrals. It is shown that owing to an ultrarelativistic dispersion relation, there is a quantum critical point governing the zero-temperature transition to a superconducting state or the exciton condensed state. Quantum transitions having critical exponents differ greatly from conventional ones and belong to the chiral universality class. We discuss the application of these results to recent experiments in which surface superconductivity was found in TIs and estimate the feasibility of phonon pairing.

We study the slow quenching dynamics (characterized by an inverse rate τ-1) of a one-dimensional transverse Ising chain with nearest neighbor ferromagentic interactions across the quantum critical point (QCP) and analyze the Loschmidt overlap measured using the subsequent temporal evolution of the final wave function (reached at the end of the quenching) with the final time-independent Hamiltonian. Studying the Fisher zeros of the corresponding generalized "partition function," we probe nonanalyticities manifested in the rate function of the return probability known as dynamical phase transitions (DPTs). In contrast to the sudden quenching case, we show that DPTs survive in the subsequent temporal evolution following the quenching across two critical points of the model for a sufficiently slow rate; furthermore, an interesting "lobe" structure of Fisher zeros emerge. We have also made a connection to topological aspects studying the dynamical topological order parameter [νD(t ) ] as a function of time (t ) measured from the instant when the quenching is complete. Remarkably, the time evolution of νD(t ) exhibits drastically different behavior following quenches across a single QCP and two QCPs. In the former case, νD(t ) increases stepwise by unity at every DPT (i.e., Δ νD=1 ). In the latter case, on the other hand, νD(t ) essentially oscillates between 0 and 1 (i.e., successive DPTs occur with Δ νD=1 and Δ νD=-1 , respectively), except for instants where it shows a sudden jump by a factor of unity when two successive DPTs carry a topological charge of the same sign.

The exhilarating spray from waves crashing into the shore, the distressing sound of a faucet leaking in the night, and the indispensable role of bubbles dissolving gas into the oceans are but a few examples of the ubiquitous presence and profound importance of drop formation and splashing in our lives. During fission, a fluid forms a neck that becomes vanishingly thin at the point of breakup. This topologicaltransition is accompanied by a dynamic singularity in which physical properties such as pressure diverge. Singularities of this sort often organize the overall dynamical evolution of nonlinear systems. I will first discuss the role of singularities in the breakup of droplets. I will then present a second experiment, selective withdrawal, in which we study the steady-state shape of a liquid as it is withdrawn by a nozzle through a surrounding fluid. Here, a change in topology may again be accompanied by a singularity. Applications of this geometry that rely on singular dynamical behavior are relevant for the coating of biological particles that may be of particular use in medical transplantation technologies.

A simple core-shell two-dimensional photonic crystal is studied where the triangle lattice symmetry and $C_{6v}$ rotation symmetry leads to rich physics in the study of accidental degeneracy's in photonic bands. We systematically evaluate different types of accidental nodal points, depending on the dispersions around them and their topological properties, when the geometry and permittivity are continuously changed. These accidental nodal points can be the critical states lying between a topological phase and a normal phase and are thus important for the study of topological photonic states. In time-reversal systems, this leads to the photonic quantum spin Hall insulator where the spin is defined upon the orbital angular momentum for transverse-magnetic polarization. We study the topological phase transition as well as the properties of the edge and bulk states and their application potentials in optics.

This paper considers a unified geometric projection approach for: 1) decomposing a general system of cooperative agents coupled via Laplacian matrices or stochastic matrices and 2) deriving a centroid-subsystem and many shape-subsystems, where each shape-subsystem has the distinct properties (e.g., preservation of formation and stability of the original system, sufficiently simple structures and explicit formation evolution of agents, and decoupling from the centroid-subsystem) which will facilitate subsequent analyses. Particularly, this paper provides an additional merit of the approach: considering adjustments of coupling topologies of agents which frequently occur in system design (e.g., to add or remove an edge, to move an edge to a new place, and to change the weight of an edge), the corresponding new shape-subsystems can be derived by a few simple computations merely from the old shape-subsystems and without referring to the original system, which will provide further convenience for analysis and flexibility of choice. Finally, such fast recalculations of new subsystems under topology adjustments are provided with examples. PMID:26955056

The energy gap in Dirac materials controls the topology and critical behaviors of the quantum phase transition associated with the critical point when the gap vanishes. However, it is often difficult to access the critical point as it requires tunablity of electronic structures. Here by exploiting the many-body screening interaction of localized spins and conduction electrons in a Kondo lattice, we demonstrate that the electronic band structures in a Kondo lattice are tunable in temperature. When spin-orbit interactions are included, we find that below the Kondo temperature, the Kondo lattice is a strong topological insulator at low temperature and undergoes a topologicaltransition to a weak topological insulator at a higher temperature TD. At TD, Dirac points emerge and the Kondo lattice becomes a Dirac semimetal. Our results indicate that the topological phase transition though a Dirac semi-metallic phase at finite temperatures also manifests profound physics and results in critical-like behavior both in magnetic and transport properties near TD. We acknowledge support from NCTS and Ministry of Science and Technology (MoST), Taiwan.

Pyrochlore iridates have attracted great interest as prime candidates that may host topologically nontrivial states, spin ice ordering and quantum spin liquid states, in particular through the interplay between different degrees of freedom, such as local moments and mobile electrons. Based on our extensive study using our high quality single crystals, we will discuss such examples, i.e. chiral spin liquid in a quadratic band touching state, Weyl semimetallic state and chiral domain wall transport nearby a quantum insulator-semimetal transition in pyrochlore iridates. This work is based on the collaboration with Nakatsuji Satoru, Kohama Yoshimitsu, Tomita Takahiro, Kindo Koichi, Jun J. Ishikawa, Balents Leon, Ishizuka Hiroaki, Timothy H. Hsieh. ZM. Tian was supported by JSPS Postdoctoral Fellowship (No.P1402).

We employ both the effective medium approximation (EMA) and Bloch theory to compare the dispersion properties of semiconductor hyperbolic metamaterials (SHMs) at mid-infrared frequencies and metallic hyperbolic metamaterials (MHMs) at visible frequencies. This analysis reveals the conditions under which the EMA can be safely applied for both MHMs and SHMs. We find that the combination of precise nanoscale layering and the longer infrared operating wavelengths puts the SHMs well within the effective medium limit and, in contrast to MHMs, allows for the attainment of very high photon momentum states. Additionally, SHMs allow for new phenomena such as ultrafast creation ofmore » the hyperbolic manifold through optical pumping. Furthermore, we examine the possibility of achieving ultrafast topologicaltransitions through optical pumping which can photo-dope appropriately designed quantum wells on the femtosecond time scale.« less

We employ both the effective medium approximation (EMA) and Bloch theory to compare the dispersion properties of semiconductor hyperbolic metamaterials (SHMs) at mid-infrared frequencies and metallic hyperbolic metamaterials (MHMs) at visible frequencies. This analysis reveals the conditions under which the EMA can be safely applied for both MHMs and SHMs. We find that the combination of precise nanoscale layering and the longer infrared operating wavelengths puts the SHMs well within the effective medium limit and, in contrast to MHMs, allows for the attainment of very high photon momentum states. Additionally, SHMs allow for new phenomena such as ultrafast creation of the hyperbolic manifold through optical pumping. Furthermore, we examine the possibility of achieving ultrafast topologicaltransitions through optical pumping which can photo-dope appropriately designed quantum wells on the femtosecond time scale.

We investigate local electronic structures of ultrathin Sb islands and their edges grown on Bi2Te2Se by scanning tunneling microscopy/spectroscopy (STM/STS) and density functional theory (DFT) calculations. The Sb islands of various thickness are grown with atomically well ordered edge structure over the 3 bilayers (BL). On the surfaces and edges of these islands, we clearly resolve edge-localized electronic states by STS measurements, which depend on the thickness. The DFT calculations identify that the strongly localized edge states of 4 and 5 BL films correspond to a quantum spin Hall (QSH) states while the edge states of 3 BL are trivial. Our experimental and theoretical results confirm the 2D topological phase transition of the ultrathin Sb films from trivial to QSH phase. Center for Artificial Low Dimensional Electronic Systems, Institute for Basic Science and Department of Physics, Pohang University of Science and Technology, Korea.

We employ both the effective medium approximation (EMA) and Bloch theory to compare the dispersion properties of semiconductor hyperbolic metamaterials (SHMs) at mid-infrared frequencies and metallic hyperbolic metamaterials (MHMs) at visible frequencies. This analysis reveals the conditions under which the EMA can be safely applied for both MHMs and SHMs. We find that the combination of precise nanoscale layering and the longer infrared operating wavelengths puts the SHMs well within the effective medium limit and, in contrast to MHMs, allows the attainment of very high photon momentum states. In addition, SHMs allow for new phenomena such as ultrafast creation of the hyperbolic manifold through optical pumping. In particular, we examine the possibility of achieving ultrafast topologicaltransitions through optical pumping which can photo-dope appropriately designed quantum wells on the femtosecond time scale.

Three-dimensionalDirac semimetals (DSMs) arematerials that have masslessDirac electrons and exhibit exotic physical properties. It has been suggested that structurally distorting a DSM can create a topological insulator but this has not yet been experimentally verified. Furthermore, Majorana fermions have been theoretically proposed to exist inmaterials that exhibit both superconductivity and topological surface states. Herewe showthat the cubic Laves phase Au2Pb has a bulk Dirac cone that is predicted to gap on cooling through a structural phase transition at 100 K. The low temperature phase can be assigned a Z(2) = -1 topological index, and this phase becomes superconducting below 1.2 K. These characteristics make Au2Pb a unique platform for studying the transition between bulk Dirac electrons and topological surface states as well as studying the interaction of superconductivity with topological surface states, combining many different properties of emergent materials-superconductivity, bulk Dirac electrons, and a topologically nontrivial Z(2) invariant.

The thermodynamic, dynamic, structural, and rigidity properties of densified liquid germania (GeO2) have been investigated using classical molecular dynamics simulation. We construct from a thermodynamic framework an analytical equation of state for the liquid allowing the possible detection of thermodynamic precursors (extrema of the derivatives of the free energy), which usually indicate the possibility of a liquid-liquid transition. It is found that for the present germania system, such precursors and the possible underlying liquid-liquid transition are hidden by the slowing down of the dynamics with decreasing temperature. In this respect, germania behaves quite differently when compared to parent tetrahedral systems such as silica or water. We then detect a diffusivity anomaly (a maximum of diffusion with changing density/volume) that is strongly correlated with changes in coordinated species, and the softening of bond-bending (BB) topological constraints that decrease the liquid rigidity and enhance transport. The diffusivity anomaly is finally substantiated from a Rosenfeld-type scaling law linked to the pair correlation entropy, and to structural relaxation. PMID:26277140

The thermodynamic, dynamic, structural, and rigidity properties of densified liquid germania (GeO{sub 2}) have been investigated using classical molecular dynamics simulation. We construct from a thermodynamic framework an analytical equation of state for the liquid allowing the possible detection of thermodynamic precursors (extrema of the derivatives of the free energy), which usually indicate the possibility of a liquid-liquid transition. It is found that for the present germania system, such precursors and the possible underlying liquid-liquid transition are hidden by the slowing down of the dynamics with decreasing temperature. In this respect, germania behaves quite differently when compared to parent tetrahedral systems such as silica or water. We then detect a diffusivity anomaly (a maximum of diffusion with changing density/volume) that is strongly correlated with changes in coordinated species, and the softening of bond-bending (BB) topological constraints that decrease the liquid rigidity and enhance transport. The diffusivity anomaly is finally substantiated from a Rosenfeld-type scaling law linked to the pair correlation entropy, and to structural relaxation.

Relative humidity (PH2O, partial pressure of water)-dependent dehydration and accompanying phase transitions in NAT-topology zeolites (natrolite, scolecite, and mesolite) were studied under controlled temperature and known PH2O conditions by in situ diffuse-reflectance infrared Fourier transform spectroscopy and parallel X-ray powder diffraction. Dehydration was characterized by the disappearance of internal H2O vibrational modes. The loss of H2O molecules caused a sequence of structural transitions in which the host framework transformation path was coupled primarily via the thermal motion of guest Na?/Ca2? cations and H2O molecules. The observation of different interactions of H2O molecules and Na?/Ca2? cations with host aluminosilicate frameworks under highand low-PH2O conditions indicated the development of different local strain fields, arising from cation H2O interactions in NAT-type channels. These strain fields influence the Si O/Al O bond strength and tilting angles within and between tetrahedra as the dehydration temperature is approached. The newly observed infrared bands (at 2,139 cm-1 in natrolite, 2,276 cm-1 in scolecite, and 2,176 and 2,259 cm-1 in mesolite) result from strong cation H2O Al Si framework interactions in NAT-type channels, and these bands can be used to evaluate the energetic evolution of Na?/Ca2? cations before and after phase transitions, especially for scolecite and mesolite. The 2,176 and 2,259 cm-1 absorption bands in mesolite also appear to be related to Na?/Ca2? order disorder that occur when mesolite loses its Ow4 H2O molecules.

There is enormous interest in engineering topological photonic systems. Despite intense activity, most works on topological photonic states (and more generally bosonic states) amount in the end to replicating a well-known fermionic single-particle Hamiltonian. Here we show how the squeezing of light can lead to the formation of qualitatively new kinds of topological states. Such states are characterized by non-trivial Chern numbers, and exhibit protected edge modes, which give rise to chiral elastic and inelastic photon transport. These topological bosonic states are not equivalent to their fermionic (topological superconductor) counterparts and, in addition, cannot be mapped by a local transformation onto topological states found in particle-conserving models. They thus represent a new type of topological system. We study this physics in detail in the case of a kagome lattice model, and discuss possible realizations using nonlinear photonic crystals or superconducting circuits. PMID:26931620

There is enormous interest in engineering topological photonic systems. Despite intense activity, most works on topological photonic states (and more generally bosonic states) amount in the end to replicating a well-known fermionic single-particle Hamiltonian. Here we show how the squeezing of light can lead to the formation of qualitatively new kinds of topological states. Such states are characterized by non-trivial Chern numbers, and exhibit protected edge modes, which give rise to chiral elastic and inelastic photon transport. These topological bosonic states are not equivalent to their fermionic (topological superconductor) counterparts and, in addition, cannot be mapped by a local transformation onto topological states found in particle-conserving models. They thus represent a new type of topological system. We study this physics in detail in the case of a kagome lattice model, and discuss possible realizations using nonlinear photonic crystals or superconducting circuits.

Optical measurement techniques are often employed to digitally capture three dimensional shapes of components. The digital data density output from these probes range from a few discrete points to exceeding millions of points in the point cloud. The point cloud taken as a whole represents a discretized measurement of the actual 3D shape of the surface of the component inspected to the measurement resolution of the sensor. Embedded within the measurement are the various features of the part that make up its overall shape. Part designers are often interested in the feature information since those relate directly to part function and to the analytical models used to develop the part design. Furthermore, tolerances are added to these dimensional features, making their extraction a requirement for the manufacturing quality plan of the product. The task of "extracting" these design features from the point cloud is a post processing task. Due to measurement repeatability and cycle time requirements often automated feature extraction from measurement data is required. The presence of non-ideal features such as high frequency optical noise and surface roughness can significantly complicate this feature extraction process. This research describes a robust process for extracting linear and arc segments from general 2D point clouds, to a prescribed tolerance. The feature extraction process generates the topology, specifically the number of linear and arc segments, and the geometry equations of the linear and arc segments automatically from the input 2D point clouds. This general feature extraction methodology has been employed as an integral part of the automated post processing algorithms of 3D data of fine features.

Topological defects play several roles in the physics of liquid crystalline matter. Their presence is felt over many length scales, necessitating modeling strategies ranging from continuum level finite element analysis of cholesteric elastomers to molecular dynamics simulation of liquid nematics. We have first studied the effect of a strain applied to a cholesteric elastomer, focusing on the transition from the twisted phase to the nematic phase, and extended work by others by including the Frank penalty for director distortions. This leads to metastability of the twisted state above the transition, prompting us to consider nucleation of topological defects as way to remove the twist walls. We explored the consequences of this idea and obtained analytical and numerical agreement, concluding that inhomogeneities in the strain field due to the coexisting phases are small, making the nucleation problem very similar to earlier studies on cholesteric liquids unwound by a magnetic field. Molecular dynamics simulations of a temperature quench of a fluid of rod-like molecules based on the Gay-Berne potential provide a way to study multiscale phenomena associated with defects, such as the structure of the core and the interaction between defect motion and the underlying orientational degrees of freedom. Locating and then studying defects in a fluid, as opposed to in a lattice simulation, however, are inherently challenging problems because of the mobility of the molecules. We have collaborated with researchers in scientific visualization to develop methods that overcome limitations of an earlier discrete finding method. In particular, new measures for describing nematic ordering are introduced, making observation of features such as the defect type and the nature of the core readily done. The dramatic improvement in spatial and temporal resolution of defect behavior afforded by the visualization opens up a number of possible routes to follow in studying static and dynamic

Geometric and mechanical properties of individual cells and interactions among neighboring cells are the basis of formation of tissue patterns. Understanding the complex interplay of cells is essential for gaining insight into embryogenesis, tissue development, and other emerging behavior. Here we describe a cell model and an efficient geometric algorithm for studying the dynamic process of tissue formation in 2D (e.g. epithelial tissues). Our approach improves upon previous methods by incorporating properties of individual cells as well as detailed description of the dynamic growth process, with all topological changes accounted for. Cell size, shape, and division plane orientation are modeled realistically. In addition, cell birth, cell growth, cell shrinkage, cell death, cell division, cell collision, and cell rearrangements are now fully accounted for. Different models of cell-cell interactions, such as lateral inhibition during the process of growth, can be studied in detail. Cellular pattern formation for monolayered tissues from arbitrary initial conditions, including that of a single cell, can also be studied in detail. Computational efficiency is achieved through the employment of a special data structure that ensures access to neighboring cells in constant time, without additional space requirement. We have successfully generated tissues consisting of more than 20,000 cells starting from 2 cells within 1 hour. We show that our model can be used to study embryogenesis, tissue fusion, and cell apoptosis. We give detailed study of the classical developmental process of bristle formation on the epidermis of D. melanogaster and the fundamental problem of homeostatic size control in epithelial tissues. Simulation results reveal significant roles of solubility of secreted factors in both the bristle formation and the homeostatic control of tissue size. Our method can be used to study broad problems in monolayered tissue formation. Our software is publicly

Control of thermal radiation at high temperatures is vital for waste heat recovery and for high-efficiency thermophotovoltaic (TPV) conversion. Previously, structural resonances utilizing gratings, thin film resonances, metasurfaces and photonic crystals were used to spectrally control thermal emission, often requiring lithographic structuring of the surface and causing significant angle dependence. In contrast, here, we demonstrate a refractory W-HfO2 metamaterial, which controls thermal emission through an engineered dielectric response function. The epsilon-near-zero frequency of a metamaterial and the connected optical topologicaltransition (OTT) are adjusted to selectively enhance and suppress the thermal emission in the near-infrared spectrum, crucial for improved TPV efficiency. The near-omnidirectional and spectrally selective emitter is obtained as the emission changes due to material properties and not due to resonances or interference effects, marking a paradigm shift in thermal engineering approaches. We experimentally demonstrate the OTT in a thermally stable metamaterial at high temperatures of 1,000 °C. PMID:27263653

We consider a tight-binding model with the nearest-neighbor hopping integrals on the honeycomb lattice in a magnetic field. Assuming one of the three hopping integrals, which we denote by ta , can take a different value from the two others, we study quantum phase structures controlled by the anisotropy of the honeycomb lattice. For weak and strong ta regions, the Hall conductances are calculated algebraically by using the Diophantine equation. Except for a few specific gaps, we completely determine the Hall conductances in these two regions including those for subband gaps. In a weak magnetic field, it is found that the weak ta region shows the unconventional quantization of the Hall conductance, σxy=-(e2/h)(2n+1) (n=0,±1,±2,…) , near the half filling, while the strong ta region shows only the conventional one, σxy=-(e2/h)n (n=0,±1,±2,…) . From the topological nature of the Hall conductance, the existence of gap closing points and quantum phase transitions in the intermediate ta region is concluded. We also study numerically the quantum phase structure in detail and find that even when ta=1 , namely, in graphene case, the system is in the weak ta phase except when the Fermi energy is located near the Van Hove singularity or the lower and upper edges of the spectrum.

A striking prediction in topological insulators is the appearance of the quantized Hall resistance when the surface states are magnetized. The surface Dirac states become gapped everywhere on the surface, but chiral edge states remain on the edges. In an applied current, the edge states produce a quantized Hall resistance that equals the Chern number C = ±1 (in natural units), even in zero magnetic field. This quantum anomalous Hall effect was observed by Chang et al. With reversal of the magnetic field, the system is trapped in a metastable state because of magnetic anisotropy. We investigate how the system escapes the metastable state at low temperatures (10 to 200 mK). When the dissipation (measured by the longitudinal resistance) is ultralow, we find that the system escapes by making a few very rapid transitions, as detected by large jumps in the Hall and longitudinal resistances. Using the field at which the initial jump occurs to estimate the escape rate, we find that raising the temperature strongly suppresses the rate. From a detailed map of the resistance versus gate voltage and temperature, we show that dissipation strongly affects the escape rate. We compare the observations with dissipative quantum tunneling predictions. In the ultralow dissipation regime, two temperature scales (T1 ~ 70 mK and T2 ~ 145 mK) exist, between which jumps can be observed. The jumps display a spatial correlation that extends over a large fraction of the sample. PMID:27482539

In two-dimensional topological insulators, helical Quantum Spin Hall (QSH) states persist even at finite magnetic fields below a critical magnetic field Bc, above which only Quantum Hall (QH) states can be found. Using linear response theory, we theoretically investigate the magneto-optical properties of inverted HgTe/CdTe quantum wells, both for infinite two-dimensional and finite-strip geometries, and possible signatures of the transition between the QSH and QH regimes. In the absorption spectrum, several peaks arise due to non-equidistant Landau levels in both regimes. However, in the QSH regime, we find an additional absorption peak at low energies in the finite-strip geometry. This peak arises due to the presence of edge states in this geometry and persists for any Fermi level in the QSH regime, while in the QH regime the peak vanishes if the Fermi level is situated in the bulk gap. Thus, by sweeping the gate voltage, it is potentially possible to distinguish between the QSH and QH regimes. Moreover, we investigate the effect of spin-orbit coupling and finite temperature on this measurement scheme. This work is supported by U.S. ONR N000141310754, DFG Grants No. SCHA 1899/1-1 and SFB 689, as well as DOE-BES DE-SC0004890.

In two-dimensional topological insulators, such as inverted HgTe/CdTe quantum wells, helical quantum spin Hall (QSH) states persist even at finite magnetic fields below a critical magnetic field Bc, above which only quantum Hall (QH) states can be found. Using linear-response theory, we theoretically investigate the magneto-optical properties of inverted HgTe/CdTe quantum wells, both for infinite two-dimensional and finite-strip geometries and for possible signatures of the transition between the QSH and QH regimes. In the absorption spectrum, several peaks arise due to nonequidistant Landau levels in both regimes. However, in the QSH regime, we find an additional absorption peak at low energies in the finite-strip geometry. This peak arises due to the presence of edge states in this geometry and persists for any Fermi level in the QSH regime, while in the QH regime the peak vanishes if the Fermi level is situated in the bulk gap. Thus, by sweeping the gate voltage, it is possible to experimentally distinguish between the QSH and QH regimes due to this signature. Moreover, we investigate the effect of spin-orbit coupling and finite temperature on this measurement scheme.

We investigate a ground state of the two-dimensional (2D) electron liquid in the presence of disorder for Landau level filling factors, for which the re-entrant integer quantum Hall effect is observed. Our particular interest is the range of filling factors, which in a clean 2D system is favorable to formation of the two-electron (2e) bubble crystal. For the smooth random potential due to charged impurities placed far away from the 2D gas, the ground state is a lightly distorted 2e bubble crystal. However, for positively or negatively charged residual impurities located approximately within about three magnetic lengths from the 2D electrons, the ground state contains charged 2e complexes formed either by positively charged impurity and 3e defect bubble, or negatively charged impurity and 2e defect bubble. In the vicinity of 1e and 3e defect bubbles, the 2e bubbles of the crystal change their shape from round to elongated forming hedgehog (for 1e defect) or vortex (for 3e defect) textures. The topological textures due to these complexes interact with vortex and hedgehog excitations, generated as temperature increases that are not bound by residual impurities. The temperature of insulator to metal transition calculated with both bound and unbound defects agrees with experiment. Research was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award DE-SC0010544.

We investigate the quantum criticality of topological phase transitions in three dimensional (3D) interacting electronic systems lacking either the time-reversal symmetry or the inversion symmetry. The minimal model, Weyl fermions with anisotropic dispersion relation, is suggested as the quantum critical theory based on the zerochirality condition. The interplay between the fermions and the long range Coulomb interaction is investigated by the standard renormalization group (RG) approach. We find that the quantum fluctuations of the anisotropic Weyl fermions induce the anisotropic partial screening of the Coulomb interaction, which eventually makes the Coulomb interaction irrelevant. It is in sharp contrast to the quantum criticality of conventional semi-metallic phases such as graphene where physical quantities receive logarithmic corrections from the marginal Coulomb interaction. Thus, the critical point is described by the non-interacting fermion theory allowing the complete theoretical understanding of the problem. The renormalized Coulomb potential shows the anisotropic power law. Its physical consequence is further illustrated by the screening problem of a charged impurity due to anisotropic Weyl fermions.

Control of thermal radiation at high temperatures is vital for waste heat recovery and for high-efficiency thermophotovoltaic (TPV) conversion. Previously, structural resonances utilizing gratings, thin film resonances, metasurfaces and photonic crystals were used to spectrally control thermal emission, often requiring lithographic structuring of the surface and causing significant angle dependence. In contrast, here, we demonstrate a refractory W-HfO2 metamaterial, which controls thermal emission through an engineered dielectric response function. The epsilon-near-zero frequency of a metamaterial and the connected optical topologicaltransition (OTT) are adjusted to selectively enhance and suppress the thermal emission in the near-infrared spectrum, crucial for improved TPV efficiency. The near-omnidirectional and spectrally selective emitter is obtained as the emission changes due to material properties and not due to resonances or interference effects, marking a paradigm shift in thermal engineering approaches. We experimentally demonstrate the OTT in a thermally stable metamaterial at high temperatures of 1,000 °C. PMID:27263653

Control of thermal radiation at high temperatures is vital for waste heat recovery and for high-efficiency thermophotovoltaic (TPV) conversion. Previously, structural resonances utilizing gratings, thin film resonances, metasurfaces and photonic crystals were used to spectrally control thermal emission, often requiring lithographic structuring of the surface and causing significant angle dependence. In contrast, here, we demonstrate a refractory W-HfO2 metamaterial, which controls thermal emission through an engineered dielectric response function. The epsilon-near-zero frequency of a metamaterial and the connected optical topologicaltransition (OTT) are adjusted to selectively enhance and suppress the thermal emission in the near-infrared spectrum, crucial for improved TPV efficiency. The near-omnidirectional and spectrally selective emitter is obtained as the emission changes due to material properties and not due to resonances or interference effects, marking a paradigm shift in thermal engineering approaches. We experimentally demonstrate the OTT in a thermally stable metamaterial at high temperatures of 1,000 °C.

A striking prediction in topological insulators is the appearance of the quantized Hall resistance when the surface states are magnetized. The surface Dirac states become gapped everywhere on the surface, but chiral edge states remain on the edges. In an applied current, the edge states produce a quantized Hall resistance that equals the Chern number C = ±1 (in natural units), even in zero magnetic field. This quantum anomalous Hall effect was observed by Chang et al. With reversal of the magnetic field, the system is trapped in a metastable state because of magnetic anisotropy. We investigate how the system escapes the metastable state at low temperatures (10 to 200 mK). When the dissipation (measured by the longitudinal resistance) is ultralow, we find that the system escapes by making a few very rapid transitions, as detected by large jumps in the Hall and longitudinal resistances. Using the field at which the initial jump occurs to estimate the escape rate, we find that raising the temperature strongly suppresses the rate. From a detailed map of the resistance versus gate voltage and temperature, we show that dissipation strongly affects the escape rate. We compare the observations with dissipative quantum tunneling predictions. In the ultralow dissipation regime, two temperature scales (T 1 ~ 70 mK and T 2 ~ 145 mK) exist, between which jumps can be observed. The jumps display a spatial correlation that extends over a large fraction of the sample. PMID:27482539

A simple core-shell two-dimensional photonic crystal is studied where the triangular lattice symmetry and the C6 point group symmetry give rich physics in accidental touching points of photonic bands. We systematically evaluate different types of accidental nodal points at the Brillouin zone center for transverse-magnetic harmonic modes when the geometry and permittivity of the core-shell material are continuously tuned. The accidental nodal points can have different dispersions and topological properties (i.e., Berry phases). These accidental nodal points can be the critical states lying between a topological phase and a normal phase of the photonic crystal. They are thus very important for the study of topological photonic states. We show that, without breaking time-reversal symmetry, by tuning the geometry of the core-shell material, a phase transition into the photonic quantum spin Hall insulator can be achieved. Here the "spin" is defined as the orbital angular momentum of a photon. We study the topological phase transition as well as the properties of the edge and bulk states and their application potentials in optics. PMID:27505772

Topological magnon insulators are a new class of magnetic materials that possess topologically nontrivial magnon bands. As a result, magnons in these materials display properties analogous to those of electrons in topological insulators. Here we present magnetization, specific heat, and neutron scattering measurements of the ferromagnetic kagome magnet Cu(1,3-bdc). Our measurements provide a detailed description of the magnetic structure and interactions in this material and confirm that it is an ideal prototype for topological magnon physics in a system with a simple spin Hamiltonian.

Van Hove singularities (VHS's) in the density of states play an outstanding and diverse role for the electronic and thermodynamic properties of crystalline solids. At the critical point the Fermi surface connectivity changes and topological properties undergo a transition. Opportunities to systematically pass a VHS at the turn of a voltage knob and study its diverse impact are however rare. With the advent of van der Waals heterostructures, control over the atomic registry of neigbouring graphene layers offers an unprecedented tool to generate a low energy VHS easily accessible with conventional gating. Here we have addressed magnetotransport when the chemical potential crosses the twist angle induced VHS in twisted bilayer graphene. A topological phase transition is experimentally disclosed in the abrupt conversion of electrons to holes or vice versa, a loss of a non-zero Berry phase and distinct sequences of integer quantum Hall states above and below the singularity.

van Hove singularities (VHS's) in the density of states play an outstanding and diverse role for the electronic and thermodynamic properties of crystalline solids. At the critical point the Fermi surface connectivity changes, and topological properties undergo a transition. Opportunities to systematically pass a VHS at the turn of a voltage knob and study its diverse impact are however rare. With the advent of van der Waals heterostructures, control over the atomic registry of neighboring graphene layers offers an unprecedented tool to generate a low energy VHS easily accessible with conventional gating. Here we have addressed magnetotransport when the chemical potential crosses the twist angle induced VHS in twisted bilayer graphene. A topological phase transition is experimentally disclosed in the abrupt conversion of electrons to holes or vice versa, a loss of a nonzero Berry phase and distinct sequences of integer quantum Hall states above and below the singularity. PMID:27387484

Metal-dielectric multilayered metamaterials are proposed to work as wideband spectral-selective emitters/absorbers due to the topological change in isofrequency contour around the epsilon-near-zero point. By setting the transition at the border between the visible and IR ranges, the metal-dielectric multilayered metamaterials become good absorbers/emitters for visible light and good reflectors for IR light, which are desirable for efficient thermal-light interconversions. PMID:26891165

We have investigated the effect of electronic topologicaltransition on the electric field-induced band gap in sliding bilayer graphene by using the density functional theory calculations. The electric field-induced band gap was found to be extremely sensitive to the electronic topologicaltransition. At the electronic topologicaltransition induced by layer sliding, four Dirac cones in the Bernal-stacked bilayer graphene reduces to two Dirac cones with equal or unequal Dirac energies depending on the sliding direction. While the critical electric field required for the band gap opening increases with increasing lateral shift for the two Dirac cones with unequal Dirac energies, the critical field is essentially zero with or without a lateral shift for the two Dirac cones with equal Dirac energies. The critical field is determined by the Dirac energy difference and the electronic screening effect. The electronic screening effect was also found to be enhanced with increasing lateral shift, apparently indicating that the massless helical and massive chiral fermions are responsible for the perfect and imperfect electronic screening, respectively. PMID:26635178

High-sensitivity (27)Al nuclear magnetic resonance (NMR) measurements of aluminum metal under hydrostatic pressure of up to 10.1 GPa reveal an unexpected negative curvature in the pressure dependence of the electronic density of states measured through shift and relaxation, which violates free electron behavior. A careful analysis of the Fermiology of aluminum shows that pressure induces an electronic topologicaltransition (Lifshitz transition) that is responsible for the measured change in the density of states. The experiments also reveal a sudden increase in the NMR linewidth above 4.2 GPa from quadrupole interaction, which is not in agreement with the metal's cubic symmetry. PMID:24292279

Evolutionary geometry of flow structures in a compressible transitional boundary layer at Ma = 0 . 7 is investigated from a Lagrangian perspective. The Lagrangian structures in the transition are extracted from the Lagrangian scalar field by a moving window filter, and then their geometry is characterized by the multi-scale and multi-directional geometric analysis (Yang and Pullin, J. Fluid Mech., 674, 2011), including the averaged inclination and sweep angles at different scales ranging from one half of the boundary layer thickness to several viscous length scales δν. The results show that averaged angles are almost unaltered for different scales before the transition. As the transition occurs, averaged inclination angles increase and sweep angles decrease rapidly with increasing reference time. Furthermore, the orientation changes more significantly for structures with small scales than large scales. In the late stage of transition, the averaged inclination angle of small-scale structures with the length scale ~ O (10) δν is 42° , and the averaged sweep angle in the logarithm law region is approximately 30° . This work is supported in part by NSFC (No. 11472015) and the Thousand Young Talent Program of China.

In order to investigate the quantum phase transition in the one-dimensional quantum compass model, we numerically calculate non-local string correlations, entanglement entropy and fidelity per lattice site by using the infinite matrix product state representation with the infinite time evolving block decimation method. In the whole range of the interaction parameters, we find that four distinct string orders characterize the four different Haldane phases and the topological quantum phase transition occurs between the Haldane phases. The critical exponents of the string order parameters β = 1/8 and the cental charges c = 1/2 at the critical points show that the topological phase transitions between the phases belong to an Ising type of universality classes. In addition to the string order parameters, the singularities of the second derivative of the ground state energies per site, the continuous and singular behaviors of the Von Neumann entropy and the pinch points of the fidelity per lattice site manifest that the phase transitions between the phases are of the second-order, in contrast to the first-order transition suggested in previous studies.

In order to investigate the quantum phase transition in the one-dimensional quantum compass model, we numerically calculate non-local string correlations, entanglement entropy and fidelity per lattice site by using the infinite matrix product state representation with the infinite time evolving block decimation method. In the whole range of the interaction parameters, we find that four distinct string orders characterize the four different Haldane phases and the topological quantum phase transition occurs between the Haldane phases. The critical exponents of the string order parameters β = 1/8 and the cental charges c = 1/2 at the critical points show that the topological phase transitions between the phases belong to an Ising type of universality classes. In addition to the string order parameters, the singularities of the second derivative of the ground state energies per site, the continuous and singular behaviors of the Von Neumann entropy and the pinch points of the fidelity per lattice site manifest that the phase transitions between the phases are of the second-order, in contrast to the first-order transition suggested in previous studies. PMID:25478955

We observe that topological defects in nematic colloids are strongly influenced by the elasticity and onset of smectic layering across the nematic (N ) to smectic-A (Sm A ) phase transition. When approaching the Sm A phase from above, the nematic hyperbolic hedgehog defect that accompanies a spherical colloidal inclusion is transformed into a focal conic line in the Sm A phase. This phase transformation has a strong influence on the pairwise colloidal interaction and is responsible for a structural transition of two-dimensional colloidal crystals. The pretransitional behavior of the point defect is supported by Landau-de Gennes Q -tensor modeling accounting for the increasing elastic anisotropy.

Fence-induced transition data simulating a raised gap filler have been acquired on the wing lower surface of a Shuttle Orbiter model in the Langley 31-Inch Mach 10 Tunnel to compare with the Shuttle Boundary Layer Transition Flight and HYTHIRM Experiments, and to provide additional correlation data for the Boundary Layer Transition Tool. In a qualitative assessment, the data exhibit the expected response to all parameter variations; however, it is unclear whether fully effective tripping at the fence was ever realized at any test condition with the present model hardware. A preliminary, qualitative comparison of the ground-based transition measurements with those obtained from the STS-128 HYTHIRM imagery at Mach 15 reveal similar transition-wake response characteristics in terms of the spreading and the path along the vehicle surface.

A direct connection between the local topology of the atomic structure of liquids and glasses and thermodynamic quantities through the atomic level stresses is suggested for metallic alloys. In particular the role of local topological instability in the phase transformation involving liquid and glass will be discussed. It is pointed out that a single local geometrical criterion can explain various phase transformations, such as melting, glass transition, and glass formation by solid state reaction and liquid quenching.

Antimicrobial peptides (AMPs) are cationic amphiphiles that comprise a key component of innate immunity. Synthetic analogues of AMPs, such as the family of phenylene ethynylene antimicrobial oligomers (AMOs), recently demonstrated broad-spectrum antimicrobial activity, but the underlying molecular mechanism is unknown. Homologues in this family can be inactive, specifically active against bacteria, or nonspecifically active against bacteria and eukaryotic cells. Using synchrotron small-angle X-ray scattering (SAXS), we show that observed antibacterial activity correlates with an AMO-induced topologicaltransition of small unilamellar vesicles into an inverted hexagonal phase, in which hexagonal arrays of 3.4-nm water channels defined by lipid tubes are formed. Polarized and fluorescence microscopy show that AMO-treated giant unilamellar vesicles remain intact, instead of reconstructing into a bulk 3D phase, but are selectively permeable to encapsulated macromolecules that are smaller than 3.4 nm. Moreover, AMOs with different activity profiles require different minimum threshold concentrations of phosphoethanolamine (PE) lipids to reconstruct the membrane. Using ternary membrane vesicles composed of DOPG:DOPE:DOPC with a charge density fixed at typical bacterial values, we find that the inactive AMO cannot generate the inverted hexagonal phase even when DOPE completely replaces DOPC. The specifically active AMO requires a threshold ratio of DOPE:DOPC = 4:1, and the nonspecifically active AMO requires a drastically lower threshold ratio of DOPE:DOPC = 1.5:1. Since most gram-negative bacterial membranes have more PE lipids than do eukaryotic membranes, our results imply that there is a relationship between negative-curvature lipids such as PE and antimicrobial hydrophobicity that contributes to selective antimicrobial activity.

An ideal hyperbolic metamaterial (HMM), which has a perfect hyperbolic dispersion curve, theoretically can support modes with indefinite wavenumbers, leading to large photon local density of states (LDOS) and many applications such as enhancing light-matter interactions, spontaneous emission and thermal radiation. Here in this presentation, HMMs based on ultrathin metal-dielectric multilayers have been studied by considering the nonlocal response of electrons in metal. Based on the hydrodynamic model of the nonlocal response, we investigate the effect of nonlocality on the performance (dispersion relation, ray refraction, LDOS and spontaneous emission) of HMMs when gradually approaching the ultrathin limit of the unit cell. We show that nonlocality will induce topologicaltransitions of the iso-frequency surfaces and limit the wavenumber as well as LDOS for both type I and type II HMMs. Under nonlocal treatment, the iso-frequency surface of type II HMM transforms from a hyperbola to a bullet shape, while for type I HMM, the surface splits into two branches: a cylindrical-like branch at high k region and an elliptical branch at the low k region. In the high k region, the nonlocality set a cut-off k for the allowed wavenumbers in both type I and type II HMMs. This cut-off k which is defined by the electron Fermi velocity of the metal intrinsically limits the LDOS and light-matter interactions. These results indicate that in the aim of achieving high performance HMMs, merely thinning the constituent films according to the local theories is no longer valid.

We present a theory of isotropic-nematic quantum phase transition in the composite Fermi liquid arising in the half-filled Landau levels. We show that the quantum phase transition is triggered by the attractive quadrupolar interaction. By performing flux attachment, system turns into a composite Fermi liquid. The nematic order parameters act as the dynamical metric interplaying with the underlying topology, the Chern-Simons theory. Here both the fluctuations of the gauge field and the nematic order parameter can soften the Fermi surface and thus the fermions form a non-Fermi liquid. The effective field theory for the isotropic-nematic phase transition has z = 3 dynamical exponent due to the Landau damping due to the finite density of the fermions. We show that there is a Berry phase term of the nematic order parameter, which can be interpreted as the ``Hall viscosity'' of the dynamical metric. We also find the Wen-Zee-like term, which effectively dresses the nematic vortex with the electric charge. Both of the terms are originated from the time reversal breaking fluctuation of the Chern-Simons gauge fields. This indicates the fluctuations of the gauge fields modify the Hall viscosity and orbital spin of the compressible half-filled Landau level.

We present a theory of the isotropic-nematic quantum phase transition in the composite Fermi liquid arising in half-filled Landau levels. We show that the quantum phase transition between the isotropic and the nematic phase is triggered by an attractive quadrupolar interaction between electrons, as in the case of conventional Fermi liquids. We derive the theory of the nematic state and of the phase transition. This theory is based on the flux attachment procedure, which maps an electron liquid in half-filled Landau levels into the composite Fermi liquid close to a nematic transition. We show that the local fluctuations of the nematic order parameters act as an effective dynamical metric interplaying with the underlying Chern-Simons gauge fields associated with the flux attachment. Both the fluctuations of the Chern-Simons gauge field and the nematic order parameter can destroy the composite fermion quasiparticles and drive the system into a non-Fermi liquid state. The effective-field theory for the isotropic-nematic phase transition is shown to have z =3 dynamical exponent due to the Landau damping of the dense Fermi system. We show that there is a Berry-phase-type term that governs the effective dynamics of the nematic order parameter fluctuations, which can be interpreted as a nonuniversal "Hall viscosity" of the dynamical metric. We also show that the effective-field theory of this compressible fluid has a Wen-Zee-type term. Both terms originate from the time-reversal breaking fluctuation of the Chern-Simons gauge fields. We present a perturbative (one-loop) computation of the Hall viscosity and also show that this term is also obtained by a Ward identity. We show that the topological excitation of the nematic fluid, the disclination, carries an electric charge. We show that a resonance observed in radio-frequency conductivity experiments can be interpreted as a Goldstone nematic mode gapped by lattice effects.

We study the tight-binding model for a graphene tube with perimeter N threaded by a magnetic field. We show exactly that this model has different nontrivial topological phases as the flux changes. The winding number, as an indicator of topological quantum phase transition (QPT) fixes at N/3 if N/3 equals to its integer part [N/3], otherwise it jumps between [N/3] and [N/3] + 1 periodically as the flux varies a flux quantum. For an open tube with zigzag boundary condition, exact edge states are obtained. There exist two perfect midgap edge states, in which the particle is completely located at the boundary, even for a tube with finite length. The threading flux can be employed to control the quantum states: transferring the perfect edge state from one end to the other, or generating maximal entanglement between them. PMID:27554930

We perform optical, surface anchoring, and textural studies of an organo-siloxane "tetrapode" material in the broad temperature range of the nematic phase. The optical, structural, and topological features are compatible with the uniaxial nematic order rather than with the biaxial nematic order, in the entire nematic temperature range -25 °C < T < 46 °C studied. For homeotropic alignment, the material experiences surface anchoring transition, but the director can be realigned into an optically uniaxial texture by applying a sufficiently strong electric field. The topological features of textures in cylindrical capillaries, in spherical droplets and around colloidal inclusions are consistent with the uniaxial character of the long-range nematic order. In particular, we observe isolated surface point defects - boojums and bulk point defects - hedgehogs that can exist only in the uniaxial nematic liquid crystal. PMID:24651889

Mo/Au transition-edge sensors exhibit weak-link behavior in the measured temperature, and field, dependence of the critical current . This is a consequence of the longitudinal proximitization between the Nb electrical bias contacts and the bilayer. Understanding how weak-link superconductivity impacts the resistive transition and the detector energy resolution is of great interest. In this contribution we present studies of for three devices that have different geometries of metallic depositions on top of the sensor used for noise mitigation and X-ray absorption. Results show that these features change the measured compared to the previously seen measurements on devices without additional deposition layers. Measurements of the small signal transition parameters and also reveal differences between designs that impact the measured response to X-rays and energy resolution.

Optics played a key role in the discovery of geometric phase. It now joins the journey of exploring topological physics, bringing bosonic topological states that equip us with the ability to make perfect photonic devices using imperfect interfaces.

We present a density functional study on the geometric structure, electronic structure, and spin transition of a series of Fe{sup II} spin-crossover (SCO) molecules, i.e., [Fe(abpt){sub 2}(NCS){sub 2}] (1), [Fe(abpt){sub 2}(NCSe){sub 2}] (2), and [Fe(dpbo)(HIm){sub 2}] (3) with dpbo diethyl(E,E)-2,2'-[1,2-phenylbis(iminomethylidyne)]bis[3-oxobutanoate](2-), N',O{sup 3},O{sup 3}', and abpt = 4-amino-3,5-bis(pyridin-2-yl)-1,2,4-triazole in order to explore more about the way to control SCO behavior of transition metal complexes. Our calculated results show that the spin transition of these Fe{sup II} molecules is accompanied with charge transfer between the Fe atom and ligands. This causes change in the electrostatic energy ({Delta}U) as well as the total electronic energy of SCO molecules. Moreover, our calculated results demonstrate an important contribution of the interionic interactions to {Delta}U, and there is the relation between {Delta}U and the thermal hysteresis behavior of SCO molecules. These results should be helpful for developing new SCO molecules.

Low-temperature magnetic phase transitions of the geometrically frustrated isosceles triangular Ising antiferromagnet CoNb2O6 have been investigated by means of neutron diffraction down to T=0.2 K under applied fields up to H∥c=4.4 kOe. Below T~0.6 K, the relaxation time of the system becomes extremely long compared with our observation time, being responsible for all the anomalous low-temperature magnetic properties observed in the bulk measurements [T. Hanawa et al., J. Phys. Soc. Jpn. 63, 2706 (1994)]. In addition to confirmation of the triple point where the antiferromagnetic, field-induced ferrimagnetic, and incommensurate phases meet together in the H∥c-T magnetic phase diagram, we also found various ordered phases that are field induced between the ferrimagnetic and saturated paramagnetic phases.

The pancreatic islet is a micro-organ that contains several thousands of endocrine cells, majority of which being the insulin releasing β - cells . - cellsareexcitablecells , andarecoupledtoeachother through gap junctional channels. Here, using percolation theory, we investigate the role of network structure in determining the dynamics of the β-cell network. We show that the β-cell synchronization depends on network connectivity. More specifically, as the site occupancy is reducing, initially the β-cell synchronization is barely affected, until it reaches around a critical value, where the synchronization exhibit a sudden rapid decline, followed by an slow exponential tail. This critical value coincides with the critical site open probability for percolation transition. The dependence over bond strength is similar, exhibiting critical-behavior like dependence around a certain value of bond strength. These results suggest that the β-cell network undergoes a dynamic phase transition when the network is percolated. We further apply the findings to study diabetes. During the development of diabetes, the β - cellnetworkconnectivitydecreases . Siteoccupancyreducesfromthe reducing β-cell mass, and the bond strength is increasingly impaired from β-cell stress and chronic hyperglycemia. We demonstrate that the network dynamics around the percolation transition explain the disease dynamics around onset, including a long time mystery in diabetes, the honeymoon phenomenon.

We study theoretically the 2D HgTe/CdTe quantum well topological insulator illuminated by circularly polarized light with frequencies higher than the difference between the equilibrium Fermi level and the bottom of the conduction band (THz range). We show that electron-hole asymmetry results in spin-dependent electric dipole transitions between edge and bulk states, and we predict an occurrence of a circular photocurrent. If the edge state is tunnel-coupled to a conductor, then the photocurrent can be detected by measuring an electromotive force in the conductor, which is proportional to the photocurrent.

BiTeI is a polar semiconductor with gigantic Rashba spin-split bands in bulk. We have investigated the effect of pressure on the electronic structure of this material via magnetotransport. Periods of Shubunikov-de Haas (SdH) oscillations originating from the spin-split outer Fermi surface and inner Fermi surface show disparate responses to pressure, while the carrier number derived from the Hall effect is unchanged with pressure. The associated parameters which characterize the spin-split band structure are strongly dependent on pressure, reflecting the pressure-induced band deformation. We find the SdH oscillations and transport response are consistent with the theoretically proposed pressure-induced band deformation leading to a topological phase transition. Our analysis suggests the critical pressure for the quantum phase transition near Pc=3.5 GPa.

When 2D electron and hole subbands in InAs/GaSb bilayers are tuned to the inverted regime the system is predicted to exhibit an insulating bulk and counter propagating helical 1D edge states. This work presents a dual-gate mapping of the topological-to-normal insulator phase transition for several InAs/GaSb bilayers wherein the InAs and GaSb layer thicknesses are varied. In-plane and out-of-plane magnetotransport experiments reveal the effect of heterostructure geometry on the magnitudes of the longitudinal and Hall magnetoresistances and on the shape and temperature dependence of the gate-tuned resistance map in the vicinity of the phase transition. This work was supported by Microsoft Research.

The expected phenomenology of noninteracting topological band insulators (TBIs) is now largely theoretically understood. However, the fate of TBIs in the presence of interactions remains an active area of research with novel, interaction-driven topological states possible, as well as new exotic magnetic states. In this work we study the magnetic phases of an exchange Hamiltonian arising in the strong interaction limit of a Hubbard model on the honeycomb lattice whose noninteracting limit is a two-dimensional TBI recently proposed for the layered heavy transition metal oxide compound (Li,Na)2IrO3. By a combination of analytical methods and exact diagonalization studies on finite-size clusters, we map out the magnetic phase diagram of the model. We find that strong spin-orbit coupling can lead to a phase transition from an antiferromagnetic Neél state to a spiral or stripy ordered state. We also discuss the conditions under which a quantum spin liquid may appear in our model, and we compare our results with the different but related Kitaev-Heisenberg-J2-J3 model which has recently been studied in a similar context.

The expected phenomenology of non-interacting topological band insulators (TBI) is now largely theoretically understood. However, the fate of TBIs in the presence of interactions remains an active area of research with novel, interaction-driven topological states possible, as well as new exotic magnetic states. In this work we study the magnetic phases of an exchange Hamiltonian arising in the strong interaction limit of a Hubbard model on the honeycomb lattice whose non-interacting limit is a two-dimensional TBI recently proposed for the layered heavy transition metal oxide compound, (Li,Na)2IrO3. By a combination of analytical methods and exact diagonalization studies on finite size clusters, we map out the magnetic phase diagram of the model. We find that strong spin-orbit coupling can lead to a phase transition from an antiferromagnetic Neél state to a spiral or stripy ordered state. We also discuss the conditions under which a quantum spin liquid may appear in our model, and we compare our results with the different but related Kitaev-Heisenberg-J2-J3 model which has recently been studied in a similar context. We gratefully acknowledge financial support from ARO Grant No. W911NF-09-1-0527 and NSF Grant No. DMR-0955778

Two-dimensional (2D) topological insulators (TIs) that exhibit quantum spin Hall effects are a new class of materials with conducting edge and insulating bulk. The conducting edge bands are spin-polarized, free of back scattering, and protected by time-reversal symmetry with potential for high-efficiency applications in spintronics. On the basis of first-principles calculations, we show that under external pressure recently synthesized stanene and germanene buckled bilayers can automatically convert into a new dynamically stable phase with flat honeycomb meshes. In contrast with the active surfaces of buckled bilayer of stanene or germanene, the above new phase is chemically inert. Furthermore, we demonstrate that these flat bilayers are 2D TIs with sizable topologically nontrivial band gaps of ∼0.1 eV, which makes them viable for room-temperature applications. Our results suggest some new design principles for searching stable large-gap 2D TIs. PMID:27149183

We report that β-InSe endowed with external strain realizes a novel three dimensional topological insulator (TI) by ab initio calculations. We predicate that the promising topological non-trivial state can be observed in an accessible temperature regime in β-InSe for its large spin-orbital band gap up to 121 meV. Specifically, unlike in previous literature where the band inversion (BI) in TIs is induced using heavy elements that have strong spin-orbital coupling (SOC), we provide a remarkable blueprint for stabilizing BI solely by mechanical deformation so that β-InSe could display BI even without considering SOC. Nevertheless, SOC is still needed to create a band gap at the crossing point by breaking the incompatibility symmetry of the inverted bands.

Here we demonstrate that both discontinuous and continuous transition between the sponge and lamellar phase can be induced by steady shear flow for a hyperswollen membrane system. The discontinuous nature of the transition is revealed by a distinct hysteresis in the rheological behavior between shear-rate increasing and decreasing measurements at a constant temperature. This discontinuity becomes weaker with an increase in the shear rate and temperature, and the transition eventually becomes a continuous one without any hysteresis. We also found another shear-induced transition in a one-phase lamellar region. The dynamic phase diagram in a nonequilibrium steady state under shear is constructed for the sponge-lamellar transition as well as another transition in a stable lamellar phase. Possible physical mechanisms for these shear-induced transitions are discussed. PMID:16605338

Interleukin-33 (IL-33) is currently the focus of multiple investigations into targeting pernicious inflammatory disorders. This mediator of inflammation plays a prevalent role in chronic disorders such as asthma, rheumatoid arthritis, and progressive heart disease. In order to better understand the possible link between the folding free energy landscape and functional regions in IL-33, a combined experimental and theoretical approach was applied. IL-33 is a pseudo- symmetrical protein composed of three distinct structural elements that complicate the folding mechanism due to competition for nucleation on the dominant folding route. Trefoil 1 constitutes the majority of the binding interface with the receptor whereas Trefoils 2 and 3 provide the stable scaffold to anchor Trefoil 1. We identified that IL-33 folds with a three-state mechanism, leading to a rollover in the refolding arm of its chevron plots in strongly native conditions. In addition, there is a second slower refolding phase that exhibits the same rollover suggesting similar limitations in folding along parallel routes. Characterization of the intermediate state and the rate limiting steps required for folding suggests that the rollover is attributable to a moving transition state, shifting from a post- to pre-intermediate transition state as you move from strongly native conditions to the midpoint of the transition. On a structural level, we found that initially, all independent Trefoil units fold equally well until a QCA of 0.35 when Trefoil 1 will backtrack in order to allow Trefoils 2 and 3 to fold in the intermediate state, creating a stable scaffold for Trefoil 1 to fold onto during the final folding transition. The formation of this intermediate state and subsequent moving transition state is a result of balancing the difficulty in folding the functionally important Trefoil 1 onto the remainder of the protein. Taken together our results indicate that the functional element of the protein is

Cosmic Topology is the name given to the study of the overall shape of the universe, which involves both global topological features and more local geometrical properties such as curvature. Whether space is finite or infinite, simply-connected or multi-connected like a torus, smaller or greater than the portion of the universe that we can directly observe, are questions that refer to topology rather than curvature. A striking feature of some relativistic, multi-connected "small" universe models is to create multiples images of faraway cosmic sources. While the most recent cosmological data fit the simplest model of a zero-curvature, infinite space model, they are also consistent with compact topologies of the three homogeneous and isotropic geometries of constant curvature, such as, for instance, the spherical Poincaré Dodecahedral Space, the flat hypertorus or the hyperbolic Picard horn. After a "dark age" period, the field of Cosmic Topology has recently become one of the major concerns in cosmology, not only for theorists but also for observational astronomers, leaving open a number of unsolved issues.

Exposure to chemicals in the environment is believed to play a critical role in the etiology of many human diseases. To enhance understanding about environmental effects on human health, the Comparative Toxicogenomics Database (CTD; http://ctdbase.org) provides unique curated data that enable development of novel hypotheses about the relationships between chemicals and diseases. CTD biocurators read the literature and curate direct relationships between chemicals-genes, genes-diseases, and chemicals-diseases. These direct relationships are then computationally integrated to create additional inferred relationships; for example, a direct chemical-gene statement can be combined with a direct gene-disease statement to generate a chemical-disease inference (inferred via the shared gene). In CTD, the number of inferences has increased exponentially as the number of direct chemical, gene and disease interactions has grown. To help users navigate and prioritize these inferences for hypothesis development, we implemented a statistic to score and rank them based on the topology of the local network consisting of the chemical, disease and each of the genes used to make an inference. In this network, chemicals, diseases and genes are nodes connected by edges representing the curated interactions. Like other biological networks, node connectivity is an important consideration when evaluating the CTD network, as the connectivity of nodes follows the power-law distribution. Topological methods reduce the influence of highly connected nodes that are present in biological networks. We evaluated published methods that used local network topology to determine the reliability of protein–protein interactions derived from high-throughput assays. We developed a new metric that combines and weights two of these methods and uniquely takes into account the number of common neighbors and the connectivity of each entity involved. We present several CTD inferences as case studies to

Based on first-principles calculations, we provide a map of the energetic stability and the electronic behavior of the topologically protected surface states of the topological insulator (TI), Bi2Se3, doped with transition metals (TMs), TM/Bi2Se3(111). We find that Fe, Mn, and Cr impurities are energetically more stable at the Bi substitutional sites, whereas we may find energetically stable substitutional as well as interstitial configurations for Co and Ni impurity atoms. Through scanning tunneling microscopy simulations, we verify that each TM atomic species and its position in the Bi2Se3(111) surface can be identified. The substitutional Fe and Cr impurities exhibit an energetic preference for the out-of-plane net magnetic moment, giving rise to a small energy gap at the Dirac point (DP), whereas the in-plane magnetic moment of substitutional Mn/Bi2Se3(111) promotes a shift of the DP from the center of the surface Brillouin zone, opening up a small energy gap. For the substitutional impurities, the shapes of the metallic bands are somewhat preserved compared with the energy bands of the pristine Bi2Se3(111) surface. Interstitial Co atoms also present an in-plane net magnetic moment, where we find the formation of metallic bands, suppressing the presence of the DP. For the Ni/Bi2Se3(111) impurity there is not a net magnetic moment, and therefore, the DP is preserved. Further formation energy results indicate other plausible (meta)stable impurity configurations, giving rise to quite different scenarios for the topological properties of TM/Bi2Se3(111), even for the same TM impurity.

We study the Hall conductance of a Chern insulator after a global quench of the Hamiltonian. The Hall conductance in the long time limit is obtained by applying the linear response theory to the diagonal ensemble. It is expressed as the integral of the Berry curvature weighted by the occupation number over the Brillouin zone. We identify a topologically driven nonequilibrium phase transition, which is indicated by the nonanalyticity of the Hall conductance as a function of the energy gap mf in the post-quench Hamiltonian Ĥf. The topological invariant for the quenched state is the winding number of the Green's function W , which equals the Chern number for the ground state of Ĥf. In the limit mf→0 , the derivative of the Hall conductance with respect to mf is proportional to ln| mf| , with the constant of proportionality being the ratio of the change of W at mf=0 to the energy gap in the initial state. This nonanalytic behavior is universal in two-band Chern insulators such as the Dirac model, the Haldane model, or the Kitaev honeycomb model in the fermionic basis.

The magnitude of ferromagnetic coupling driven by inter-band (Bloembergen-Rowland - BR) and intra-band (Ruderman-Kittel-Kasuya-Yoshida - RKKY) spin polarization is evaluated within kp theory for topological semimetals Hg1-xMnxTe and Hg1-xMnxSe as well as for 3D Dirac semimetal (Cd1-xMnx)3As2. In these systems Mn2+ ions do not introduce any carriers. Since, however, both conduction and valence bands are built from anion p-type wave functions, hybridization of Mn d levels with neighboring anion p states leads to spin-dependent p - d coupling of both electrons and holes to localized Mn spins, resulting in sizable inter-band spin polarization and, thus in large BR interactions. We demonstrate that this ferromagnetic coupling, together with antiferromagnetic superexchange, elucidate a specific dependence of spin-glass freezing temperature on x, determined experimentally for these systems. Furthermore, by employing a multi-orbital tight-binding method, we find that superexchange becomes ferromagnetic when Mn is replaced by Cr or V. Since Cr should act as an isoelectronic impurity in HgTe, this opens a road for realization of ferromagnetic topological insulators based on (Hg,Cr)Te.

In a topological insulator (TI), if one of its heavy elements is replaced by a light one, the spin-orbit coupling (SOC) strength decreases and eventually the TI transforms into a normal insulator beyond a critical level of substitution.This is the standard description of the topological phase transition (TPT). However, this notion of TPT, driven solely by the SOC (or something equivalent), is not complete for finite size samples considering that the thickness of the topological surface states diverges at the critical point. Here, on specially-engineered (BixIn1-x)2 Se3 thin films, using systematic transport measurments we show that not only the SOC but also the finite sample size can induce TPT. This study sheds light on the role of spatial confinement as an extra tuning parameter controlling the topological critical point.

The semimetal-to-semiconductor transition in fcc-Yb under modest pressure can be considered a picture book example of a metal-insulator transition of the Lifshitz type. We have performed transport measurements at low temperatures in the closest vicinity of the transition and related DFT calculations of the Fermi surface. Our resistivity measurements show a linear temperature dependence with an unusually low dρ / dT at low temperatures approaching the MIT. The calculations suggest fcc-ytterbium being an ultra-multi valley system with 24 electron and 6 hole pockets in the Brillouin zone. Such Fermi surface topology naturally supports the appearance of strongly correlated phases. An estimation of the quasiparticle-enhanced effective mass shows that the scattering rate is by at least two orders of magnitude lower than in other materials which exhibit linear-in-T behavior at a quantum critical point. However, we cannot exclude an excessive effective mass enhancement, when the van Hove singularity touches the Fermi level.

The electronic states and topological behaviors of Pt(Ni, Pd)-decorated silicene are investigated by using an ab-initio method. All the three kinds of the adatoms prefer hollow sites of the silicene, guaranteeing the Dirac cones unbroken. The Pt(Ni, Pd)-decorated silicene systems all present quantum valley Hall (QVH) states with the gap opened exactly at the Fermi level. The gaps of the QVH states can be increased substantially by applying a positive electric field. Very fascinating phase transitions from QVH to quantum spin Hall (QSH) and then to QVH again are achieved in the Pt/Ni-decorated silicene when a negative electric field is applied. The QSH state in the Pd case with a negative electric field is, however, quenched because of relatively larger Rashba spin-orbit coupling (SOC) than the intrinsic SOC in the system. Our findings may be useful for the applications of silicene-based devices in valleytronics and spintronics.

The Schwinger boson theory of the frustrated square lattice antiferromagnet yields a stable, gapped Z2 spin liquid ground state with time-reversal symmetry, incommensurate spin correlations, and long-range Ising-nematic order. We obtain an equivalent description of this state using fermionic spinons (the fermionic spinons can be considered to be bound states of the bosonic spinons and the visons). Upon doping, the Z2 spin liquid can lead to a fractionalized Fermi liquid (FL*) with small Fermi pockets of electronlike quasiparticles, while preserving the Z2 topological and Ising-nematic orders. We describe a Higgs transition out of this deconfined metallic state into a confining superconducting state which is almost always of the Fulde-Ferrell-Larkin-Ovchinnikov type, with spatial modulation of the superconducting order.

The hydrothermal reaction of uranyl nitrate with rubidium nitrate and arsenic (III) oxide results in the formation of polymorphic α- and β-Rb[UO{sub 2}(AsO{sub 3}OH)(AsO{sub 2}(OH){sub 2})]·H{sub 2}O (α-, β-RbUAs) and the anhydrous phase Rb[UO{sub 2}(AsO{sub 3}OH)(AsO{sub 2}(OH){sub 2})] (RbUAs). These phases were structurally, chemically and spectroscopically characterized. The structures of all three compounds are based upon topologically identical, but geometrically isomeric layers. The layers are linked with each other by means of the Rb cations and hydrogen bonding. Dehydration experiments demonstrate that water deintercalation from hydrous α- and β-RbUAs yields anhydrous RbUAs via topotactic reactions. - Graphical abstract: Three different layer geometries observed in the structures of Rb[UO{sub 2}(AsO{sub 3}OH)(AsO{sub 2}(OH){sub 2})] and α- and β- Rb[UO{sub 2}(AsO{sub 3}OH)(AsO{sub 2}(OH){sub 2})]·H{sub 2}O. Two different coordination environments of uranium polyhedra (types I and II) are shown schematically on the top of the figure. - Highlights: • Three new uranyl arsenates were synthesized from the hydrothermal reactions. • The phases consist of the topologically identical but geometrically different layers. • Topotactic transitions were observed in the processes of mono-hyrates dehydration.

It can be shown that the dynamics of the Landau-Zener model can be accurately described in terms of the Kibble-Zurek theory of the topological defect production in nonequilibrium phase transitions. The simplest quantum model exhibiting the Kibble-Zurek mechanism is presented. A new intuitive description of Landau-Zener dynamics is found.

The human genome is segmented into topologically associating domains (TADs), but the role of this conserved organization during transient changes in gene expression is not known. Here we describe the distribution of progestin-induced chromatin modifications and changes in transcriptional activity over TADs in T47D breast cancer cells. Using ChIP-seq (chromatin immunoprecipitation combined with high-throughput sequencing), Hi-C (chromosome capture followed by high-throughput sequencing), and three-dimensional (3D) modeling techniques, we found that the borders of the ∼2000 TADs in these cells are largely maintained after hormone treatment and that up to 20% of the TADs could be considered as discrete regulatory units where the majority of the genes are either transcriptionally activated or repressed in a coordinated fashion. The epigenetic signatures of the TADs are homogeneously modified by hormones in correlation with the transcriptional changes. Hormone-induced changes in gene activity and chromatin remodeling are accompanied by differential structural changes for activated and repressed TADs, as reflected by specific and opposite changes in the strength of intra-TAD interactions within responsive TADs. Indeed, 3D modeling of the Hi-C data suggested that the structure of TADs was modified upon treatment. The differential responses of TADs to progestins and estrogens suggest that TADs could function as “regulons” to enable spatially proximal genes to be coordinately transcribed in response to hormones. PMID:25274727

The folding topology of DNA G-quadruplexes (G4s) depends not only on their nucleotide sequences but also on environmental factors and/or ligand binding. Here, a G4 ligand, 3,6-bis(1-methyl-4-vinylpyridium iodide)-9-(1-(1-methyl-piperidinium iodide)-3,6,9-trioxaundecane) carbazole (BMVC-8C3O), can induce topological conversion of non-parallel to parallel forms in human telomeric DNA G4s. Nuclear magnetic resonance (NMR) spectroscopy with hydrogen-deuterium exchange (HDX) reveals the presence of persistent imino proton signals corresponding to the central G-quartet during topological conversion of Tel23 and Tel25 G4s from hybrid to parallel forms, implying that the transition pathway mainly involves local rearrangements. In contrast, rapid HDX was observed during the transition of 22-CTA G4 from an anti-parallel form to a parallel form, resulting in complete disappearance of all the imino proton signals, suggesting the involvement of substantial unfolding events associated with the topologicaltransition. Site-specific imino proton NMR assignments of Tel23 G4 enable determination of the interconversion rates of individual guanine bases and detection of the presence of intermediate states. Since the rate of ligand binding is much higher than the rate of ligand-induced topological conversion, a three-state kinetic model was evoked to establish the associated energy diagram for the topological conversion of Tel23 G4 induced by BMVC-8C3O. PMID:26975658

The folding topology of DNA G-quadruplexes (G4s) depends not only on their nucleotide sequences but also on environmental factors and/or ligand binding. Here, a G4 ligand, 3,6-bis(1-methyl-4-vinylpyridium iodide)-9-(1-(1-methyl-piperidinium iodide)-3,6,9-trioxaundecane) carbazole (BMVC-8C3O), can induce topological conversion of non-parallel to parallel forms in human telomeric DNA G4s. Nuclear magnetic resonance (NMR) spectroscopy with hydrogen-deuterium exchange (HDX) reveals the presence of persistent imino proton signals corresponding to the central G-quartet during topological conversion of Tel23 and Tel25 G4s from hybrid to parallel forms, implying that the transition pathway mainly involves local rearrangements. In contrast, rapid HDX was observed during the transition of 22-CTA G4 from an anti-parallel form to a parallel form, resulting in complete disappearance of all the imino proton signals, suggesting the involvement of substantial unfolding events associated with the topologicaltransition. Site-specific imino proton NMR assignments of Tel23 G4 enable determination of the interconversion rates of individual guanine bases and detection of the presence of intermediate states. Since the rate of ligand binding is much higher than the rate of ligand-induced topological conversion, a three-state kinetic model was evoked to establish the associated energy diagram for the topological conversion of Tel23 G4 induced by BMVC-8C3O. PMID:26975658

We discover a topological phase transition between conventional s+- and s++ superconducting phases by tuning the ratio of electron--electron and electron--phonon coupling constants in an FeAs-type two-band structure. Proving the existence of this unexpected quantum criticality within the mean-field theory, we propose that the quantum critical point be identified with a critical spin liquid state of an ``extended'' Dirac spectrum, where critical superconducting fluctuations cause screening of charge degrees of freedom for electronic excitations, which allows spinon excitations to carry only the spin quantum number 1/2. The emergence of the critical spin liquid state at the s+--s++ superconducting quantum critical point leads us to predict a metal--insulator--metal crossover behavior in electrical resistivity above the superconducting transition temperatures as the ratio of the electron--electron and electron--phonon coupling constants is increased. In addition, we uncover that the competition between electron--electron repulsion and electron--phonon attraction gives rise to a huge enhancement of the superconducting transition temperature near the quantum critical point which is several hundreds percent larger than that of the case when only one of the two is taken into account. Our renormalization group analysis claims that this mechanism for the enhancement of the critical temperature is not limited to superconductivity but can be applied to various Fermi surface instabilities, proposing an underlying universal structure, which turns out to be essentially identical to that of a recent study [Phys. Rev. Lett. 108 (2012) 046601] on the enhancement of the Kondo temperature in the presence of Rashba spin--orbit interaction. We speculate that the existence of this possible ``deconfined'' quantum criticality can be verified not only theoretically but also experimentally, particularly, in Li2(Pd1-xPtx)3B superconductors, varying x from 0 to 1.

The first-principles band theory paradigm has been a key player not only in the process of discovering new classes of topologically interesting materials, but also for identifying salient characteristics of topological states, enabling direct and sharpened confrontation between theory and experiment. This review begins by discussing underpinnings of the topological band theory, which involve a layer of analysis and interpretation for assessing topological properties of band structures beyond the standard band theory construct. Methods for evaluating topological invariants are delineated, including crystals without inversion symmetry and interacting systems. The extent to which theoretically predicted properties and protections of topological states have been verified experimentally is discussed, including work on topological crystalline insulators, disorder and interaction driven topological insulators (TIs), topological superconductors, Weyl semimetal phases, and topological phase transitions. Successful strategies for new materials discovery process are outlined. A comprehensive survey of currently predicted 2D and 3D topological materials is provided. This includes binary, ternary, and quaternary compounds, transition metal and f -electron materials, Weyl and 3D Dirac semimetals, complex oxides, organometallics, skutterudites, and antiperovskites. Also included is the emerging area of 2D atomically thin films beyond graphene of various elements and their alloys, functional thin films, multilayer systems, and ultrathin films of 3D TIs, all of which hold exciting promise of wide-ranging applications. This Colloquium concludes by giving a perspective on research directions where further work will broadly benefit the topological materials field.

A quantum object can acquire a geometric phase (such as Berry phases and Aharonov–Bohm phases) when evolving along a path in a parameter space with non-trivial gauge structures. Inherent to quantum evolutions of wavepackets, quantum diffusion occurs along quantum trajectories. Here we show that quantum diffusion can also be geometric as characterized by the imaginary part of a geometric phase. The geometric quantum diffusion results from interference between different instantaneous eigenstate pathways which have different geometric phases during the adiabatic evolution. As a specific example, we study the quantum trajectories of optically excited electron-hole pairs in time-reversal symmetric insulators, driven by an elliptically polarized terahertz field. The imaginary geometric phase manifests itself as elliptical polarization in the terahertz sideband generation. The geometric quantum diffusion adds a new dimension to geometric phases and may have applications in many fields of physics, e.g., transport in topological insulators and novel electro-optical effects. PMID:26178745

A quantum object can acquire a geometric phase (such as Berry phases and Aharonov-Bohm phases) when evolving along a path in a parameter space with non-trivial gauge structures. Inherent to quantum evolutions of wavepackets, quantum diffusion occurs along quantum trajectories. Here we show that quantum diffusion can also be geometric as characterized by the imaginary part of a geometric phase. The geometric quantum diffusion results from interference between different instantaneous eigenstate pathways which have different geometric phases during the adiabatic evolution. As a specific example, we study the quantum trajectories of optically excited electron-hole pairs in time-reversal symmetric insulators, driven by an elliptically polarized terahertz field. The imaginary geometric phase manifests itself as elliptical polarization in the terahertz sideband generation. The geometric quantum diffusion adds a new dimension to geometric phases and may have applications in many fields of physics, e.g., transport in topological insulators and novel electro-optical effects. PMID:26178745

This dissertation reports that arbitrary Boolean logic equations and operators can be represented in geometric algebra as linear equations composed entirely of orthonormal vectors using only addition and multiplication Geometric algebra is a topologically based algebraic system that naturally incorporates the inner and anticommutative outer products into a real valued geometric product, yet does not rely on complex numbers or matrices. A series of custom tools was designed and built to simplify geometric algebra expressions into a standard sum of products form, and automate the anticommutative geometric product and operations. Using this infrastructure, quantum bits (qubits), quantum registers and EPR-bits (ebits) are expressed symmetrically as geometric algebra expressions. Many known quantum computing gates, measurement operators, and especially the Bell/magic operators are also expressed as geometric products. These results demonstrate that geometric algebra can naturally and faithfully represent the central concepts, objects, and operators necessary for quantum computing, and can facilitate the design and construction of quantum computing tools.

A continuous deformation of a Hamiltonian possessing at low energy two Dirac points of opposite chiralities can lead to a gap opening by merging the two Dirac points. In two dimensions, the critical Hamiltonian possesses a semi-Dirac spectrum: linear in one direction but quadratic in the other. We study the transport properties across such a transition, from a Dirac semimetal through a semi-Dirac phase toward a gapped phase. Using both a Boltzmann approach and a diagrammatic Kubo approach, we describe the conductivity tensor within the diffusive regime. In particular, we show that both the anisotropy of the Fermi surface and the Dirac nature of the eigenstates combine to give rise to anisotropic transport times, manifesting themselves through an unusual matrix self-energy.

We propose a scheme to dynamically synthesize a space-periodic effective magnetic field for neutral atoms by time-periodic magnetic field pulses. When atomic spin adiabatically follows the direction of the effective magnetic field, an adiabatic scalar potential together with a geometric vector potential emerges for the atomic center-of-mass motion, due to the Berry phase effect. While atoms hop between honeycomb lattice sites formed by the minima of the adiabatic potential, complex Peierls phase factors in the hopping coefficients are induced by the vector potential, and these phase factors facilitate a topological Chern insulator. With further tuning of external parameters, both a topological phase transition and topological flat bands can be achieved, highlighting realistic prospects for studying strongly correlated phenomena in this system. Our Letter presents an alternative pathway towards creating and manipulating topological states of ultracold atoms by magnetic fields. PMID:27104703

We propose a scheme to dynamically synthesize a space-periodic effective magnetic field for neutral atoms by time-periodic magnetic field pulses. When atomic spin adiabatically follows the direction of the effective magnetic field, an adiabatic scalar potential together with a geometric vector potential emerges for the atomic center-of-mass motion, due to the Berry phase effect. While atoms hop between honeycomb lattice sites formed by the minima of the adiabatic potential, complex Peierls phase factors in the hopping coefficients are induced by the vector potential, and these phase factors facilitate a topological Chern insulator. With further tuning of external parameters, both a topological phase transition and topological flat bands can be achieved, highlighting realistic prospects for studying strongly correlated phenomena in this system. Our Letter presents an alternative pathway towards creating and manipulating topological states of ultracold atoms by magnetic fields.

The introduction of magnetism in SnTe-class topological crystalline insulators is a challenging subject with great importance in the quantum device applications. Based on the first-principles calculations, we have studied the defect energetics and magnetic properties of 3 d transition-metal (TM)-doped SnTe. We find that the doped TM atoms prefer to stay in the neutral states and have comparatively high formation energies, suggesting that the uniform TMdoping in SnTe with a higher concentration will be difficult unless clustering. In the dilute doping regime, all the magnetic TMatoms are in the high-spin states, indicating that the spin splitting energy of 3 d TM is stronger than the crystal splitting energy of the SnTe ligand. Importantly, Mn-doped SnTe has relatively low defect formation energy, largest local magnetic moment, and no defect levels in the bulk gap, suggesting that Mn is a promising magnetic dopant to realize the magnetic order for the theoretically-proposed large-Chern-number quantum anomalous Hall effect (QAHE) in SnTe.

Total energy local density calculations for the effects of pressure on the lattice parameters, bond lengths, electronic structure, and {ital A}{sub 1{ital g}} phonon frequency in HgBa{sub 2}CuO{sub 4} have been carried out in order to understand the role of pressure in increasing the {ital T}{sub {ital c}} of mercury-based superconductors. Theoretically determined zero-pressure lattice parameters and phonon frequencies are found to be in good agreement with experiment. An electronic topologicaltransition is found to occur when the van Hove singularity (vHS) is shifted close to the vicinity of {ital E}{sub {ital F}} by pressure which causes considerable phonon softening and anomalous behavior of the {ital c}-axis length, the Hg-O(2) bond, and the Ba {ital z} coordinate. A set of experiments that might be able to detect the presence of the vHS close to {ital E}{sub {ital F}} is proposed. {copyright} {ital 1996 The American Physical Society.}

Using the Angell model of broken bonds (configurons), configuron clustering in a topologically disordered lattice (network) of amorphous SiO{sub 2} and GeO{sub 2} upon a glass-liquid transition is considered. It is shown that the glass-liquid transition is accompanied by the formation of a macroscopic (percolation) configuron cluster penetrating the entire bulk of the material and possessing fractal geometry. The glass-liquid (overcooled liquid) percolation phase transition in the amorphous substance is accompanied by a change in the Hausdorff dimension of the bond network structure for configurons from the three-dimensional Euclidean dimension in the glassy state to a fractal dimension of 2.55 {+-} 0.05 in the liquidlike state. Contrary to the kinetic character of the liquid-glass transition, the glass-transition temperature is a thermodynamic parameter of the amorphous substance, depending parametrically on the cooling rate.

In order to characterize the pressure-induced decomposition of ringwoodite (γ-Mg2SiO4), the topological analysis of the electron density ρ( r), based upon the theory of atoms in molecules (AIM) developed by Bader in the framework of the catastrophe theory, has been performed. Calculations have been carried out by means of the ab initio CRYSTAL09 code at the HF/DFT level, using Hamiltonians based on the Becke- LYP scheme containing hybrid Hartree-Fock/density functional exchange-correlation terms. The equation of state at 0 K has been constructed for the three phases involved in the post-spinel phase transition (ringwoodite → Mg-perovskite + periclase) occurring at the transition zone-lower mantel boundary. The topological results show that the decomposition of the ringwoodite at high pressures is caused by a conflict catastrophe. Furthermore, topological evidences of the central role played by the oxygen atoms to facilitate the pressure-induced ringwoodite decomposition and the subsequent phase transition have been noticed.

In a three-dimensional topological insulator Bi2Se3, a stress control for band gap manipulation was predicted but no systematic investigation has been performed yet due to the requirement of large external stress. We report herein on the strain-dependent results for Bi2Se3 films of various thicknesses that are grown via a self-organized ordering process. Using small angle X-ray scattering and Raman spectroscopy, the changes of d-spacings in the crystal structure and phonon vibration shifts resulted from stress are clearly observed when the film thickness is below ten quintuple layers. From the UV photoemission/inverse photoemission spectroscopy (UPS/IPES) results and ab initio calculations, significant changes of the Fermi level and band gap were observed. The deformed band structure also exhibits a Van Hove singularity at specific energies in the UV absorption experiment and ab initio calculations. Our results, including the synthesis of a strained ultrathin topological insulator, suggest a new direction for electronic and spintronic applications for the future.In a three-dimensional topological insulator Bi2Se3, a stress control for band gap manipulation was predicted but no systematic investigation has been performed yet due to the requirement of large external stress. We report herein on the strain-dependent results for Bi2Se3 films of various thicknesses that are grown via a self-organized ordering process. Using small angle X-ray scattering and Raman spectroscopy, the changes of d-spacings in the crystal structure and phonon vibration shifts resulted from stress are clearly observed when the film thickness is below ten quintuple layers. From the UV photoemission/inverse photoemission spectroscopy (UPS/IPES) results and ab initio calculations, significant changes of the Fermi level and band gap were observed. The deformed band structure also exhibits a Van Hove singularity at specific energies in the UV absorption experiment and ab initio calculations. Our

We introduce a topological quantum number—coined dynamical topological order parameter (DTOP)—that is dynamically defined in the real-time evolution of a quantum many-body system and represented by a momentum space winding number of the Pancharatnam geometric phase. Our construction goes conceptually beyond the standard notion of topological invariants characterizing the wave function of a system, which are constants of motion under coherent time evolution. In particular, we show that the DTOP can change its integer value at discrete times where so called dynamical quantum phase transitions occur, thus serving as a dynamical analog of an order parameter. Interestingly, studying quantum quenches in one-dimensional two-banded Bogoliubov-de Gennes models, we find that the DTOP is capable of resolving if the topology of the system Hamiltonian has changed over the quench. Furthermore, we investigate the relation of the DTOP to the dynamics of the string order parameter that characterizes the topology of such systems in thermal equilibrium.

Topologically protected fermionic quasiparticles appear in metals, where band degeneracies occur at the Fermi level, dictated by the band structure topology. While in some metals these quasiparticles are direct analogues of elementary fermionic particles of the relativistic quantum field theory, other metals can have symmetries that give rise to quasiparticles, fundamentally different from those known in high-energy physics. Here, we report on a new type of topological quasiparticles—triple point fermions—realized in metals with symmorphic crystal structure, which host crossings of three bands in the vicinity of the Fermi level protected by point group symmetries. We find two topologically different types of triple point fermions, both distinct from any other topological quasiparticles reported to date. We provide examples of existing materials that host triple point fermions of both types and discuss a variety of physical phenomena associated with these quasiparticles, such as the occurrence of topological surface Fermi arcs, transport anomalies, and topological Lifshitz transitions.

We have constructed the geometric phases emerging from the non-trivial topology of a space-dependent magnetic field B(r), interacting with the spin magnetic moment of a neutral particle. Our basic tool, adapted from a previous work on Berry’s phases, is the space-dependent unitary transformation {U}({\\mathbf {r}}), which leads to the identity, {U}({\\mathbf {r}})^{\\dag }\\, {\\mathbf {S}}\\,{\\bm \\cdot}\\, {\\mathbf {B}}({\\mathbf {r}}) \\, {U}({\\mathbf {r}}) = \\vert {\\mathbf {B}}({\\mathbf {r}}) \\vert \\, S_z, at each point r. In the ‘rotated’ Hamiltonian \\widehat{ H}, \\frac{ \\partial }{\\partial {\\mathbf {r}}} is replaced by the non-Abelian covariant derivative \\frac{ \\partial }{\\partial {\\mathbf {r}}}- \\frac{i}{\\hbar } {A}({\\mathbf {r}}) where {A}({\\mathbf {r}}) = i \\hbar \\, {U}^{\\dag }\\,{\\bm\\cdot}\\, \\frac{ \\partial }{\\partial {\\mathbf {r}}} {U} can be written as A1(r)Sx + A2(r)Sy + A3(r)Sz. The Abelian differentials Ak(r)·dr are given in terms of the Euler angles defining the orientation of B(r). The non-Abelian field {A}({\\mathbf {r}}) transforms as a Yang-Mills field; however, its vanishing ‘curvature’ reveals its purely geometric character. We have defined a perturbation scheme based upon the assumption that in \\widehat{ H} the longitudinal field A3(r) dominates the transverse field A1, 2(r) contributions, evaluated to second order. The geometry embedded in both the vector field A3(r) and the geometric magnetic field \\mathbf { B}_3 ({\\mathbf {r}}) = \\frac{ \\partial }{\\partial {\\mathbf {r}}}\\wedge {{\\mathbf {A}}}_3({\\mathbf {r}}) is described by their associated Aharonov-Bohm phase. As an illustration we study the physics of cold 171Yb atoms dressed by overlaying two circularly polarized stationary waves with orthogonal directions, which form a 2D square optical lattice. The frequency is tuned midway between the two hyperfine levels of the (6s6p)3P1 states to protect the optical B(r) field generated by the

In a three-dimensional topological insulator Bi2Se3, a stress control for band gap manipulation was predicted but no systematic investigation has been performed yet due to the requirement of large external stress. We report herein on the strain-dependent results for Bi2Se3 films of various thicknesses that are grown via a self-organized ordering process. Using small angle X-ray scattering and Raman spectroscopy, the changes of d-spacings in the crystal structure and phonon vibration shifts resulted from stress are clearly observed when the film thickness is below ten quintuple layers. From the UV photoemission/inverse photoemission spectroscopy (UPS/IPES) results and ab initio calculations, significant changes of the Fermi level and band gap were observed. The deformed band structure also exhibits a Van Hove singularity at specific energies in the UV absorption experiment and ab initio calculations. Our results, including the synthesis of a strained ultrathin topological insulator, suggest a new direction for electronic and spintronic applications for the future. PMID:26659120

Background and Aims The impact of a fruit tree's architecture on its performance is still under debate, especially with regard to the definition of varietal ideotypes and the selection of architectural traits in breeding programmes. This study aimed at providing proof that a modelling approach can contribute to this debate, by using in silico exploration of different combinations of traits and their consequences on light interception, here considered as one of the key parameters to optimize fruit tree production. Methods The variability of organ geometrical traits, previously described in a bi-parental population, was used to simulate 1- to 5-year-old apple trees (Malus × domestica). Branching sequences along trunks observed during the first year of growth of the same hybrid trees were used to initiate the simulations, and hidden semi-Markov chains previously parameterized were used in subsequent years. Tree total leaf area (TLA) and silhouette to total area ratio (STAR) values were estimated, and a sensitivity analysis was performed, based on a metamodelling approach and a generalized additive model (GAM), to analyse the relative impact of organ geometry and lateral shoot types on STAR. Key Results A larger increase over years in TLA mean and variance was generated by varying branching along trunks than by varying organ geometry, whereas the inverse was observed for STAR, where mean values stabilized from year 3 to year 5. The internode length and leaf area had the highest impact on STAR, whereas long sylleptic shoots had a more significant effect than proleptic shoots. Although the GAM did not account for interactions, the additive effects of the geometrical factors explained >90% of STAR variation, but much less in the case of branching factors. Conclusions This study demonstrates that the proposed modelling approach could contribute to screening architectural traits and their relative impact on tree performance, here viewed through light interception. Even

Functionalized X-Bi bilayers (X = Ga, In, and Tl) with halogens bonded on their both sides have been recently claimed to be the giant topological insulators due to the strong band inversion strengths. Employing the first-principles electronic structure calculation, we find the topological band order transition from the order p - p - s of the X-Bi bilayers with halogens on their both sides to the new order p - s - p of the bilayers (especially for X = Ga and In) with halogen on one side and hydrogen on the other side, where the asymmetric hydrogen bonding simulates the substrate. We further find that the p - s bulk band gap of the bilayer bearing the new order p - s - p sensitively depends on the electric field, which enables a meaningful engineering of the quantum spin Hall edge state by controlling the external electric field. PMID:27623710

We report the recent progress on the theoretical aspects of monolayer topological insulators including silicene, germanene and stanene, which are monolayer honeycomb structures of silicon, germanium and tin, respectively. They show quantum spin Hall effects in nature due to the spin-orbit interaction. The band gap can be tuned by applying perpendicular electric field, which induces a topological phase transition. We also analyze the topological properties of generic honeycomb systems together with the classification of topological insulators. Phase diagrams of topological insulators and superconductors in honeycomb systems are explicitly determined. We also investigate topological electronics including a topological field-effect transistor, the topological Kirchhoff's law and the topological spin-valleytronics.

The morphologic transition from complex impact craters, to peak-ring basins, and to multi-ring basins has been well-documented for decades. Less clear has been the morphometric characteristics of these landforms due to their large size and the lack of global high-resolution topography data. We use data from the Lunar Orbiter Laser Altimeter (LOLA) instrument onboard the Lunar Reconnaissance Orbiter (LRO) spacecraft to derive the morphometric characteristics of impact basins on the Moon, assess the trends, and interpret the processes involved in the observed morphologic transitions. We first developed a new technique for measuring and calculating the geometric/morphometric properties of impact basins on the Moon. This new method meets a number of criteria that are important for consideration in any topographic analysis of crater landforms (e.g., multiple data points, complete range of azimuths, systematic, reproducible analysis techniques, avoiding effects of post-event processes, robustness with respect to the statistical techniques). The resulting data more completely capture the azimuthal variation in topography that is characteristic of large impact structures. These new calculations extend the well-defined geometric trends for simple and complex craters out to basin-sized structures. Several new geometric trends for peak-ring basins are observed. Basin depth: A factor of two reduction in the depth to diameter (d/Dr) ratio in the transition from complex craters to peak-ring basins may be characterized by a steeper trend than known previously. The d/Dr ratio for peak-ring basins decreases with rim-crest diameter, which may be due to a non-proportional change in excavation cavity growth or scaling, as may occur in the simple to complex transition, or increased magnitude of floor uplift associated with peak-ring formation. Wall height, width, and slope: Wall height and width increase with increasing rim-crest diameter, while wall slope decreases; decreasing ratios

The Fisher–Rao metric from information geometry is related to phase transition phenomena in classical statistical mechanics. Several studies propose to extend the use of information geometry to study more general phase transitions in complex systems. However, it is unclear whether the Fisher–Rao metric does indeed detect these more general transitions, especially in the absence of a statistical model. In this paper we study the transitions between patterns in the Gray-Scott reaction–diffusion model using Fisher information. We describe the system by a probability density function that represents the size distribution of blobs in the patterns and compute its Fisher information with respect to changing the two rate parameters of the underlying model. We estimate the distribution non-parametrically so that we do not assume any statistical model. The resulting Fisher map can be interpreted as a phase-map of the different patterns. Lines with high Fisher information can be considered as boundaries between regions of parameter space where patterns with similar characteristics appear. These lines of high Fisher information can be interpreted as phase transitions between complex patterns.

The search for an intrinsic single crystal topological superconductor is one of the most dynamic areas of modern condensed matter physics. One of the best candidates of such a material is Tl5Te3 (Tc = 2 . 3 K), which previous ARPES measurements have shown possesses a Dirac cone within its superconducting gap. However, the fundamental nature of superconductivity, i.e. the superconducting order parameter, in Tl5Te3 remains unknown. Additionally, it has been shown that Tl5Te3 undergoes a superconducting-insulator transition upon doping with Sn. With no band parity inversion expected in the fully Sn doped compound one expects a topological supercondutor - trivial insulator transition, the nature of which is also unknown. In this work we use highly sensitive microwave cavity perturbation measurements, a direct probe of the superfluid density, to study the low energy electrodynamics of superconductivity in Tl5Te3 and its corresponding superconductor-insulator transition upon Sn doping. Work at Johns Hopkins was supported by the Gordon and Betty Moore Foundation through Grant GBMF2628, the DOE-BES through DE-FG02-08ER46544, and the ARCS Foundation.

We examine the topological properties of a spin–singlet superconductor with Rashba and Dresselhaus (110) spin–orbit couplings. We demonstrate that there are several topological invariants in the Bogoliubov–de Gennes (BdG) Hamiltonian by symmetry analysis. In particular, the Pfaffian invariant P for the particle–hole symmetry can be used to demonstrate all the possible phase diagrams of the BdG Hamiltonian. We find that the edge spectrum is either Dirac cone or flat band which supports the emergence of the Majorana fermion in this system. For the Majorana flat bands, an edge index, namely the Pfaffian invariant P(k{sub y}) or the winding number W(k{sub y}), is needed to make them topologically stable. These edge indices can also be used in determining the location of the Majorana flat bands. - Highlights: • Majorana fermion can emerge in the spin–orbit coupled singlet superconductor. • Pfaffian invariant and 1D winding number can be used to identify the nontrivial topological phase where Majorana flat band exists. • All the possible phase diagrams in the spin–orbit coupled singlet superconductor are demonstrated. • Majorana flat band only exists in the y direction in our model. • Majorana flat band has a significant experimental signature in the tunneling conductance measurement.

A stibarsen [derived from Latin stibium (antimony) and arsenic] or allemontite, is a natural form of arsenic antimonide (SbAs) with the same layered structure as arsenic and antimony. Thus, exploring the two-dimensional SbAs nanosheets is of great importance to gain insights into the properties of group V-V compounds at the atomic scale. Here, we propose a class of two-dimensional V-V honeycomb binary compounds, SbAs monolayers, which can be tuned from semiconductor to topological insulator. By ab initio density functional theory, both α-SbAs and γ-SbAs display a significant direct band gap, while others are indirect semiconductors. Interestingly, in an atomically thin β-SbAs polymorph, spin-orbital coupling is significant, which reduces its band gap by 200 meV. Especially under biaxial tensile strain, the gap of β-SbAs can be closed and reopened with concomitant change of band shapes, which is reminiscent of band inversion known in many topological insulators. In addition, we find that the Z2 topological invariant is 1 for β-SbAs under the tensile strain of 12%, and the nontrivial topological feature of β-SbAs is also confirmed by the gapless edge states which cross linearly at the Γ point. These ultrathin group-V-V semiconductors with outstanding properties are highly favorable for applications in alternative optoelectronic and quantum spin Hall devices.

This paper surveys the use of geometric methods for wireless sensor networks. The close relationship of sensor nodes with their embedded physical space imposes a unique geometric character on such systems. The physical locations of the sensor nodes greatly impact on system design in all aspects, from low-level networking and organization to high-level information processing and applications. This paper reviews work in the past 10 years on topics such as network localization, geometric routing, information discovery, data-centric routing and topology discovery. PMID:22124080

It has been shown that both humanly constructed and natural networks are often characterized by small-world phenomenon and assortative mixing. In this paper, we propose a geometrically growing model for small-world networks. The model displays both tunable small-world phenomenon and tunable assortativity. We obtain analytical solutions of relevant topological properties such as order, size, degree distribution, degree correlation, clustering, transitivity, and diameter. It is also worth noting that the model can be viewed as a generalization for an iterative construction of Farey graphs. PMID:24578661

In this Chapter, a novel bidirectional algorithm for hybrid (discrete + continuous-time) Lie-Hamiltonian evolution in adaptive energy landscape-manifold is designed and its topological representation is proposed. The algorithm is developed within a geometrically and topologically extended framework of Hopfield's neural nets and Haken's synergetics (it is currently designed in Mathematica, although with small changes it could be implemented in Symbolic C++ or any other computer algebra system). The adaptive energy manifold is determined by the Hamiltonian multivariate cost function H, based on the user-defined vehicle-fleet configuration matrix W, which represents the pseudo-Riemannian metric tensor of the energy manifold. Search for the global minimum of H is performed using random signal differential Hebbian adaptation. This stochastic gradient evolution is driven (or, pulled-down) by `gravitational forces' defined by the 2nd Lie derivatives of H. Topological changes of the fleet matrix W are observed during the evolution and its topological invariant is established. The evolution stops when the W-topology breaks down into several connectivity-components, followed by topology-breaking instability sequence (i.e., a series of phase transitions).

For the resistive pressure-gradient-driven turbulence model, the transition from laminar regime to fully developed turbulence is not simple and goes through several phases. For low values of the plasma parameter {beta}, a single quasicoherent structure forms. As {beta} increases, several of these structures may emerge and in turn take the dominant role. Finally, at high {beta}, fully developed turbulence with a broad spectrum is established. A suitable characterization of this transition can be given in terms of topological properties of the flow. Here, we analyze these properties that provide an understanding of the turbulence-induced transport and give a measure of the breaking of the homogeneity of the turbulence. To this end, an approach is developed that allows discriminating between topological properties of plasma turbulence flows that are relevant to the transport dynamics and the ones that are not. This is done using computational homology tools and leads to a faster convergence of numerical results for a fixed level of resolution than previously presented in Phys. Rev. E 78, 066402 (2008)

This thesis contains several applications of the first-principles electronic-structure theory with special emphasis in parts of the thesis on the geometrical aspects of the theory. We start by reviewing the basics of the first-principles electronic-structure methods which are then used throughout the thesis. The first application of these methods is on the analysis of the stability and lattice dynamics of alpha- and beta-cristobalite phases of SiO2. We also map the complete low-energy landscape connecting these two structures and give implications on the phase transition in this compound. Next we study a family of Pbnm perovskites that are promising candidates for silicon-compatible high-K dielectrics. We calculate their structure and dielectric response, and compare with experimental results where available. The third application of these methods is to the large isosymmetric reorientation of oxygen octahedra rotation axes in epitaxially strained perovskites. We explain the origin of the peculiar energy landscape topology as a function of epitaxial strain. In the part of the thesis devoted to the geometrical aspects of electronic structure theory, we begin by extending the concept of electronic polarization to a Chern insulators. These insulators are characterized by a non-zero off-diagonal sigma_xy conductivity tensor component, quantized in units of e 2/h. Finally we discuss another geometrical quantity, the Chern-Simons orbital magnetoelectric coupling. We present a first-principles based calculation of this quantity in several compounds, and motivated by recent developments in the theory of topological insulators, we speculate about the existence of "large-theta materials," in which this kind of coupling could be unusually large.

Eight new coordination polymers (CPs), namely, [Zn(1,2-mbix)(tbtpa)]n (1), [Co(1,2-mbix)(tbtpa)]n (2), [CdCl(1,2-mbix)(tbtpa)0.5]n (3), {[Cd(1,2-bix)(tbtpa)]·H2O}n (4), {[Cd0.5(1,2-bix)(tbtpa)0.5]·H2O}n (5), {[Co0.5(1,2-bix)(tbtpa)0.5]·2H2O}n (6), {[Co(1,2-bix)(tbtpa)]·H2O}n (7) and {[Co(1,2-bix)(tbtpa)]·Diox·2H2O}n (8), were synthesized under solvothermal conditions based on mix-ligand strategy (H2tbtpa=tetrabromoterephthalic acid and 1,2-mbix=1,2-bis((2-methyl-1H-imidazol-1-yl)methyl)benzene, 1,2-bix=1,2-bis(imidazol-1-ylmethyl)benzene). All of the CPs have been structurally characterized by single-crystal X-ray diffraction analyses and further characterized by elemental analyses, IR spectroscopy, powder X-ray diffraction (PXRD), and thermogravimetric analyses (TGA). X-ray diffraction analyses show that 1 and 2 are isotypics which have 2D highly undulated networks with (4,4)-sql topology with the existence of C-H &ctdot;Br interactions; for 3, it has a 2D planar network with (4,4)-sql topology with the occurrence of C-H &ctdot;Cl interactions other than C-H &ctdot;Br interactions; 4 shows a 3D 2-fold interpenetrated nets with rare 65·8-mok topology which has a self-catention property. As the same case as 1 and 2, 5 and 6 are also isostructural with planar layers with 44-sql topology which further assembled into 3D supramolecular structure through the interdigitated stacking fashion and the C-Br &ctdot;Cph interactions. As for 7, it has a 2D slightly undulated networks with (4,4)-sql topology which has one dimension channel. While 8 has a 2-fold interpenetrated networks with (3,4)-connect jeb topology with point symbol {63}{65·8}. And their structures can be tuned by conformations of bis(imidazol) ligands and solvent mixture. Besides, the TGA properties for all compounds and the luminescent properties for 1, 3, 4, 5 are discussed in detail.

Living systems are characterized by complexity in structure and emergent dynamic orders. In many aspects the onset of a chronic disease resembles phase transition in a dynamic system: quantitative changes accumulate largely unnoticed until a critical threshold is reached, which causes abrupt qualitative changes of the system. In this study we investigate this idea in a real example, the insulin-producing pancreatic islet β-cells and the onset of type 1 diabetes. Within each islet, the β-cells are electrically coupled to each other, and function as a network with synchronized actions. Using percolation theory we show how normal islet function is intrinsically linked to network connectivity, and the critical point where the islet cellular network loses site percolation, is consistent with laboratory and clinical observations of the threshold β-cell loss that causes islet functional failure. Numerical simulations confirm that the islet cellular network needs to be percolated for β-cells to synchronize. Furthermore, the interplay between site percolation and bond strength predicts the existence of a transient phase of islet functional recovery after disease onset and introduction of treatment, potentially explaining a long time mystery in the clinical study of type 1 diabetes: the honeymoon phenomenon. Based on these results, we hypothesized that the onset of T1D may be the result of a phase transition of the islet β-cell network. We further discuss the potential applications in identifying disease-driving factors, and the critical parameters that are predictive of disease onset.

A geometric interpretation of the Berry phase and its Wilczek-Zee non-Abelian generalization are given in terms of connections on principal fiber bundles. It is demonstrated that a principal fiber bundle can be trivial in all cases, while the connection and its holonomy group are nontrivial. Therefore, the main role is played by geometric rather than topological effects.

This chapter shall discuss the basics and the applications of geometrical optical methods in modern optics. Geometrical optics has a long tradition and some ideas are many centuries old. Nevertheless, the invention of modern personal computers which can perform several million floating-point operations in a second also revolutionized the methods of geometrical optics and so several analytical methods lost importance whereas numerical methods such as ray tracing became very important. Therefore, the emphasis in this chapter is also on modern numerical methods such as ray tracing and some other systematic methods such as the paraxial matrix theory.

Topological insulator (TI) states have been demonstrated in materials with a narrow gap and large spin-orbit interactions (SOI). Here we demonstrate that nanoscale engineering can also give rise to a TI state, even in conventional semiconductors with a sizable gap and small SOI. Based on advanced first-principles calculations combined with an effective low-energy k∙p Hamiltonian, we show that the intrinsic polarization of materials can be utilized to simultaneously reduce the energy gap and enhance the SOI, driving the system to a TI state. The proposed system consists of ultrathin InN layers embedded into GaN, a layer structure that is experimentally achievable.

The breaking of time reversal symmetry in a topological insulator (TI) by magnetic doping is one of the most studied phenomena among the properties of Dirac materials. The robustness of the topological surface states (TSS) against magnetic impurities is of critical importance for spin-dependent transport in these systems. The interaction between TSS and magnetic impurities can open a gap, provided that the magnetic order is oriented normal to the surface of the TI. Such gap opening is crucial for realizing TI-based spintronic devices and for the observation of different fundamental phenomena, such as the anomalous quantum Hall effect. Using density functional theory as implemented in the WIEN2k ab-initio package, we have investigated the effect of the magnetization orientation on the gap opening at the Dirac point, for substitutional Mn and Fe impurities on the Bi2Se3 surface, and have calculated the associated single-ion anisotropy (SIA). We also have studied bulk SIA in order to compare the role played by TSS on the surface SIA.

By applying high temperature (1270 K) and high pressure (3.5 GPa), significant changes occur in the structural volume and crystal topology of ThMo2 O8 , allowing the formation of an unexpected new ThMo2 O8 polymorph (high-temperature/high-pressure (HT/HP) orthorhombic ThMo2 O8 ). Compared with the other three ThMo2 O8 polymorphs prepared at the ambient pressure (monoclinic, orthorhombic, and hexagonal phases), the molar volume for the quenched HT/HP-orthorhombic ThMo2 O8 is decreased by almost 20 %. As a result of such a dramatic structural transformation, a permanent high-pressure quenchable state is able to be sustained when the pressure is released. The crystal structures of the three ambient ThMo2 O8 phases are based on three-dimensional (3D) frameworks constructed from corner-sharing ThOx (x=6, 8, or 9) polyhedra and MoO4 tetrahedra. The HT/HP-orthorhombic ThMo2 O8 , however, crystallizes in a novel structural topology, exhibiting very dense arrangements of ThO11 and MoO4+1 polyhedra connecting along the crystallographic c axis. The phase transitions among all four of these ThMo2 O8 polymorphs are unveiled and fully characterized with regard to the structural transformation, thermal stability, and vibrational properties. The complementary first principles calculations of Gibbs free energies reveal the underlying energetics of the phase transition, which support the experimental findings. PMID:26626413

As transparent conducting oxides (TCOs), In2O3 in the high pressure phase attracts extensive research interests. Because physical properties are determined by the geometric structures, we investigate the electronic and optical properties of Zn/Sn codoped In2O3 materials (IZTO) being modulated by the bixbyite/corundum phase transition via Density Functional Theory calculations. For IZTO in high pressure phase, i.e. corundum phase, Sn/Zn dopant pair tends to form face-sharing ZnO6 and SnO6 octahedrons. The radius differences between Zn2+/Sn4+ dopants and In3+ host cations make Jahn-Teller effect occur and IZTO transform from bixbyite to corundum phase under a slight higher pressure than that of pure In2O3. Although Zn/Sn cosubstitution of In ions may increase the free carrier effective mass m * near the band edge, when IZTO crystal transforms to corundum phase, the more dense packing structure results in stronger cation s-orbital overlaps than in bixbyite phase, which makes m * recover to a smaller value. In addition, corundum IZTO has a larger indirect band gap and a high dopant solubility. So these investigations may open a new way to search for TCOs materials with low indium content.

Desert roses are gypsum crystals that consist of intersecting disks. We determine their geometrical structure using computer assisted tomography. By mapping the geometrical structure onto a graph, the topology of the desert rose is analyzed and compared to a model based on diffusion limited aggregation. By comparing the topology, we find that the model gets a number of the features of the real desert rose right, whereas others do not fit so well.

Kibble-Zurek mechanism (KZM) uses critical scaling to predict density of topological defects and other excitations created in second order phase transitions. We point out that simply inserting asymptotic critical exponents deduced from the immediate vicinity of the critical point to obtain predictions can lead to results that are inconsistent with a more careful KZM analysis based on causality – on the comparison of the relaxation time of the order parameter with the “time distance” from the critical point. As a result, scaling of quench-generated excitations with quench rates can exhibit behavior that is locally (i.e., in the neighborhood of any given quench rate) well approximated by the power law, but with exponents that depend on that rate, and that are quite different from the naive prediction based on the critical exponents relevant for asymptotically long quench times. Kosterlitz-Thouless scaling (that governs e.g. Mott insulator to superfluid transition in the Bose-Hubbard model in one dimension) is investigated as an example of this phenomenon. PMID:25091996

The content of this talk is twofold. In the first part, we provide a paradigm of efficient numerical evaluation scheme for topological invariants via zero-frequency single-particle Green's function in quantum Monte Carlo (QMC) simulations. Especially, we introduce a periodization process to overcome the ubiquitous finite-size effect and make use of symmetry properties of the underlying systems to reduce the computational effort. This scheme is tested to be successful on models of interacting topological insulators, where there is single-particle gap closing at the transition. In the second part, we apply the above scheme to wider classes of interacting topological insulators, in which the breakdown of constructing topological invariant via single-particle Green's functions is presented. These systems host novel interaction-driven topological phase transitions without symmetry breaking, and hence fermionic degree of freedom is not involved at the critical point, instead, collective bosonic mode become critical.

We realized a quantum geometric "charge" pump for a Bose-Einstein condensate (BEC) in the lowest Bloch band of a novel bipartite magnetic lattice. Topological charge pumps in filled bands yield quantized pumping set by the global-topological-properties of the bands. In contrast, our geometric charge pump for a BEC occupying just a single crystal momentum state exhibits nonquantized charge pumping set by local-geometrical-properties of the band structure. Like topological charge pumps, for each pump cycle we observed an overall displacement (here, not quantized) and a temporal modulation of the atomic wave packet's position in each unit cell, i.e., the polarization. PMID:27258857

Classically, all topologies are allowed as solutions to the Einstein equations. However, one does not observe any topological structures on medium range distance scales, that is scales that are smaller than the size of the observed universe but larger than the microscopic scales for which quantum gravity becomes important. Recently, Friedman, Schleich and Witt (1993) have proven that there is topological censorship on these medium range distance scales: the Einstein equations, locally positive energy, and local predictability of physics imply that any medium distance scale topological structures cannot be seen. More precisely we show that the topology of physically reasonable isolated systems is shrouded from distant observers, or in other words there is a topological censorship principle.

We show that a class of exactly solvable quantum Ising models, including the transverse-field Ising model and anisotropic X Y model, can be characterized as the loops in a two-dimensional auxiliary space. The transverse-field Ising model corresponds to a circle and the X Y model corresponds to an ellipse, while other models yield cardioid, limacon, hypocycloid, and Lissajous curves etc. It is shown that the variation of the ground state energy density, which is a function of the loop, experiences a nonanalytical point when the winding number of the corresponding loop changes. The winding number can serve as a topological quantum number of the quantum phases in the extended quantum Ising model, which sheds some light upon the relation between quantum phase transition and the geometrical order parameter characterizing the phase diagram.

We show that a class of exactly solvable quantum Ising models, including the transverse-field Ising model and anisotropic XY model, can be characterized as the loops in a two-dimensional auxiliary space. The transverse-field Ising model corresponds to a circle and the XY model corresponds to an ellipse, while other models yield cardioid, limacon, hypocycloid, and Lissajous curves etc. It is shown that the variation of the ground state energy density, which is a function of the loop, experiences a nonanalytical point when the winding number of the corresponding loop changes. The winding number can serve as a topological quantum number of the quantum phases in the extended quantum Ising model, which sheds some light upon the relation between quantum phase transition and the geometrical order parameter characterizing the phase diagram. PMID:26551140

The phase transition, elastic and electronic properties of three phases (phase I, II, and III) of Sb2Te3 are investigated by using the generalized gradient approximation (GGA) with the PBESOL exchange-correlation functional in the framework of density-functional theory. Some basic physical parameters, such as lattice constants, bulk modulus, shear modulus, Young’s modulus, Poisson’s ratio, acoustic velocity, and Debye temperature Θ are calculated. The obtained lattice parameters under various pressures are consistent with experimental data. Phase transition pressures are 9.4 GPa (I → II) and 14.1 GPa (II → III), which are in agreement with the experimental results. According to calculated elastic constants, we also discuss the ductile or brittle characters and elastic anisotropies of three phases. Phases I and III are brittle, while phase II is ductile. Of the three phases, phase II has the most serious degree of elastic anisotropy and phase III has the slightest one. Finally, we investigate the partial densities of states (PDOSs) of three phases and find that the three phases possess some covalent features. Project supported by the National Natural Science Foundation of China (Grant Nos. 11204192 and 11174214) and Jointly supported by the National Natural Science Foundation of China and the China Academy of Engineering Physics (NSAF) (Grant No. U1430117).

This paper develops information geometric representations for nonlinear filters in continuous time. The posterior distribution associated with an abstract nonlinear filtering problem is shown to satisfy a stochastic differential equation on a Hilbert information manifold. This supports the Fisher metric as a pseudo-Riemannian metric. Flows of Shannon information are shown to be connected with the quadratic variation of the process of posterior distributions in this metric. Apart from providing a suitable setting in which to study such information-theoretic properties, the Hilbert manifold has an appropriate topology from the point of view of multi-objective filter approximations. A general class of finite-dimensional exponential filters is shown to fit within this framework, and an intrinsic evolution equation, involving Amari's -1-covariant derivative, is developed for such filters. Three example systems, one of infinite dimension, are developed in detail.

Two high-pressure phases of a potassium gallosilicate with a gismondine framework (K-GaSi-GIS) were characterized using Rietveld refinements of in-situ high-pressure, high-resolution synchrotron X-ray powder diffraction data. The observed response of the K-GaSi-GIS framework under hydrostatic pressure is a gradual flattening of the so-called "double crankshaft" structural chain units. At pressures below 1.0(1) GPa, additional water molecules from the hydrostatic pressure-transmitting medium are inserted into the potassium-water guest network ("pressure-induced hydration") resulting in a "super-hydrated" high-pressure phase I. As the flattening of the double crankshaft structural units in the GIS framework continues above 1.6 GPa, the ellipticity of the cross-linking 8-ring windows is reduced below a certain threshold, and a disordering of the potassium-water guest structure along the 8-ring channel, characteristic of a disordered high-pressure phase II, is observed. The concerted framework distortion and guest network disordering accommodates the increased hydration level while maintaining the seven-fold coordination environment of the potassium cations to framework oxygen atoms and water molecules. We have thus established the atomistic details of a guest-host order-disorder transition under pressure-induced hydration conditions in a zeolite with GIS framework and compared it to other zeolites during pressure-induced hydration. We find that the structural changes mediated by the extra-framework cations and their coordination environment under PIH conditions are at the core of these different mechanisms and are driving the changes in the ellipticity of pore openings, order-disorder and disorder-order transitions, and framework distortions. PMID:18266365

We consider extended Hubbard models with repulsive interactions on a honeycomb lattice, and the transitions from the semimetal to Mott insulating phases at half-filling. Because of the frustrated nature of the second-neighbor interactions, topological Mott phases displaying the quantum Hall and the quantum spin Hall effects are found for spinless and spin fermion models, respectively. The mean-field phase diagram is presented and the fluctuations are treated within the random phase approximation. Renormalization group analysis shows that these states can be favored over the topologically trivial Mott insulating states.

We report a detailed low-temperature study of the two-dimensional (2D) electron gas in a 6.1-nm-wide HgTe quantum well with H g0.3C d0.7Te barriers by terahertz magnetophotoconductivity and magnetotransmission combined with magnetotransport measurements (Rx x and Rx y) in magnetic fields up to 10 T. This well width, close to that at the topological phase transition, corresponds to conventional band ordering, and we probe the "bulk" quasi-2D Landau-level (LL) spectrum of the conduction band at high energies (≈135 -160 meV ) above the Dirac point. The calculated separations between adjacent LLs of the same spin based on published parameters for this structure are in fair agreement with the measured cyclotron resonance energies. However, the very large spin splittings observed (Espin>Ecyclotron) require a significantly larger g -parameter ge for electrons. Tilted field coincidence experiments are consistent with the large spin splitting showing coincidences at 3/2 and twice the cyclotron energy. This large value of ge also leads to interesting crossings of the calculated LLs, and we find direct evidence of these crossings in the Rx x measurements at lower electron densities (Fermi energies) produced by negative gate bias.

Iron-based compounds (IBS) display a surprising variety of superconducting properties that seems to arise from the strong sensitivity of these systems to tiny details of the lattice structure. In this respect, systems that become superconducting under pressure, like CaFe2As2, are of particular interest. Here we report on the first directional point-contact Andreev-reflection spectroscopy (PCARS) measurements on CaFe2As2 crystals under quasi-hydrostatic pressure, and on the interpretation of the results using a 3D model for Andreev reflection combined with ab-initio calculations of the Fermi surface (within the density functional theory) and of the order parameter symmetry (within a random-phase-approximation approach in a ten-orbital model). The almost perfect agreement between PCARS results at different pressures and theoretical predictions highlights the intimate connection between the changes in the lattice structure, a topologicaltransition in the holelike Fermi surface sheet, and the emergence on the same sheet of an order parameter with a horizontal node line. PMID:27216477

Iron-based compounds (IBS) display a surprising variety of superconducting properties that seems to arise from the strong sensitivity of these systems to tiny details of the lattice structure. In this respect, systems that become superconducting under pressure, like CaFe2As2, are of particular interest. Here we report on the first directional point-contact Andreev-reflection spectroscopy (PCARS) measurements on CaFe2As2 crystals under quasi-hydrostatic pressure, and on the interpretation of the results using a 3D model for Andreev reflection combined with ab-initio calculations of the Fermi surface (within the density functional theory) and of the order parameter symmetry (within a random-phase-approximation approach in a ten-orbital model). The almost perfect agreement between PCARS results at different pressures and theoretical predictions highlights the intimate connection between the changes in the lattice structure, a topologicaltransition in the holelike Fermi surface sheet, and the emergence on the same sheet of an order parameter with a horizontal node line. PMID:27216477

We study optical, structural, and surface anchoring properties of thermotropic nematic bent-core material A131. The focus is on the features associated with orientational order as the material has been reported to exhibit not only the usual uniaxial nematic but also the biaxial nematic phase. We demonstrate that A131 experiences a surface anchoring transition from a perpendicular to tilted alignment when the temperature decreases. The features of the tilted state are consistent with surface-induced birefringence associated with smectic layering near the surface and a molecular tilt that changes along the normal to the substrates. The surface-induced birefringence is reduced to zero by a modest electric field that establishes a uniform uniaxial nematic state. Both refractive and absorptive optical properties of A131 are consistent with the uniaxial order. We found no evidence of the “polycrystalline” biaxial behavior in the cells placed in crossed electric and magnetic fields. We observe stable topological point defects (boojums and hedgehogs) and nonsingular “escaped” disclinations pertinent only to the uniaxial order. Finally, freely suspended films of A131 show uniaxial nematic and smectic textures; a decrease in the film thickness expands the temperature range of stability of smectic textures, supporting the idea of surface-induced smectic layering. Our conclusion is that A131 features only a uniaxial nematic phase and that the apparent biaxiality is caused by subtle surface effects rather than by the bulk biaxial phase.

Iron-based compounds (IBS) display a surprising variety of superconducting properties that seems to arise from the strong sensitivity of these systems to tiny details of the lattice structure. In this respect, systems that become superconducting under pressure, like CaFe2As2, are of particular interest. Here we report on the first directional point-contact Andreev-reflection spectroscopy (PCARS) measurements on CaFe2As2 crystals under quasi-hydrostatic pressure, and on the interpretation of the results using a 3D model for Andreev reflection combined with ab-initio calculations of the Fermi surface (within the density functional theory) and of the order parameter symmetry (within a random-phase-approximation approach in a ten-orbital model). The almost perfect agreement between PCARS results at different pressures and theoretical predictions highlights the intimate connection between the changes in the lattice structure, a topologicaltransition in the holelike Fermi surface sheet, and the emergence on the same sheet of an order parameter with a horizontal node line.

Present LANDSAT data formats are reviewed to clarify how the geodetic location and registration capabilities were defined for P-tape products and RBV data. Since there is only one geometric model used in the master data processor, geometric location accuracy of P-tape products depends on the absolute accuracy of the model and registration accuracy is determined by the stability of the model. Due primarily to inaccuracies in data provided by the LANDSAT attitude management system, desired accuracies are obtained only by using ground control points and a correlation process. The verification of system performance with regards to geodetic location requires the capability to determine pixel positions of map points in a P-tape array. Verification of registration performance requires the capability to determine pixel positions of common points (not necessarily map points) in 2 or more P-tape arrays for a given world reference system scene. Techniques for registration verification can be more varied and automated since map data are not required. The verification of LACIE extractions is used as an example.

Many tools to analyze and represent high dimensional data already exits yet most of them are not flexible, informative and intuitive enough to help the scientists make the corresponding analysis and predictions, understand the structure and complexity of scientific data, get a complete picture of it and explore a greater number of hypotheses. With this in mind, N-Dimensional Data Analysis and Visualization (ND²AV) is being developed to serve as an interactive visual analysis platform with the purpose of coupling together a number of these existing tools that range from statistics, machine learning, and data mining, with new techniques, in particular with new visualization approaches. My task is to create the rendering and implementation of a new concept called topological spines in order to extend ND²AV's scope. Other existing visualization tools create a representation preserving either the topological properties or the structural (geometric) ones because it is challenging to preserve them both simultaneously. Overcoming such challenge by creating a balance in between them, the topological spines are introduced as a new approach that aims to preserve them both. Its render using OpenGL and C++ and is currently being tested to further on be implemented on ND²AV. In this paper I will present what are the Topological Spines and how they are rendered.

Frustrated magnetism is an exciting and diverse field in condensed matter physics that has grown tremendously over the past 20 years. This special issue aims to capture some of that excitement in the field of geometrically frustrated magnets and is inspired by the 2010 Highly Frustrated Magnetism (HFM 2010) meeting in Baltimore, MD, USA. Geometric frustration is a broad phenomenon that results from an intrinsic incompatibility between some fundamental interactions and the underlying lattice geometry based on triangles and tetrahedra. Most studies have centred around the kagomé and pyrochlore based magnets but recent work has looked at other structures including the delafossite, langasites, hyper-kagomé, garnets and Laves phase materials to name a few. Personally, I hope this issue serves as a great reference to scientist both new and old to this field, and that we all continue to have fun in this very frustrated playground. Finally, I want to thank the HFM 2010 organizers and all the sponsors whose contributions were an essential part of the success of the meeting in Baltimore. Geometrically frustrated magnetism contents Spangolite: an s = 1/2 maple leaf lattice antiferromagnet? T Fennell, J O Piatek, R A Stephenson, G J Nilsen and H M Rønnow Two-dimensional magnetism and spin-size effect in the S = 1 triangular antiferromagnet NiGa2S4 Yusuke Nambu and Satoru Nakatsuji Short range ordering in the modified honeycomb lattice compound SrHo2O4 S Ghosh, H D Zhou, L Balicas, S Hill, J S Gardner, Y Qi and C R Wiebe Heavy fermion compounds on the geometrically frustrated Shastry-Sutherland lattice M S Kim and M C Aronson A neutron polarization analysis study of moment correlations in (Dy0.4Y0.6)T2 (T = Mn, Al) J R Stewart, J M Hillier, P Manuel and R Cywinski Elemental analysis and magnetism of hydronium jarosites—model kagome antiferromagnets and topological spin glasses A S Wills and W G Bisson The Herbertsmithite Hamiltonian: μSR measurements on single crystals

Topological information has proven very valuable in the analysis of scientific data. An important challenge that remains is presenting this highly abstract information in a way that it is comprehensible even if one does not have an in-depth background in topology. Furthermore, it is often desirable to combine the structural insight gained by topological analysis with complementary information, such as geometric information. We present an overview over methods that use metaphors to make topological information more accessible to non-expert users, and we demonstrate their applicability to a range of scientific data sets. With the increasingly complex output of exascale simulations, the importance of having effective means of providing a comprehensible, abstract overview over data will grow. The techniques that we present will serve as an important foundation for this purpose.

We report a systematic angle-resolved photoemission spectroscopy on topological insulator (TI) TlBi1 -xSbxTe2 which is bulk insulating at 0.5 ≲x ≲0.9 and undergoes a metal-insulator-metal transition with the Sb content x . We found that this transition is characterized by a systematic hole doping with increasing x , which results in the Fermi-level crossings of the bulk conduction and valence bands at x ˜0 and x ˜1 , respectively. The Dirac point of the topological surface state is gradually isolated from the valence-band edge, accompanied by a sign reversal of Dirac carriers. We also found that the Dirac velocity is the largest among known solid-solution TI systems. The TlBi1 -xSbxTe2 system thus provides an excellent platform for Dirac-cone engineering and device applications of TIs.

An algorithm is presented which describes an application independent method for reducing the number of polygonal primitives required to faithfully represent an object. Reducing polygon count without a corresponding reduction in object detail is important for: achieving interactive frame rates in scientific visualization, reducing mass storage requirements, and facilitating the transmission of large, multi-timestep geometric data sets. This paper shows how coplanar and nearly coplanar polygons can be merged into larger complex polygons and re-triangulated into fewer simple polygons than originally required. The notable contributions of this paper are: (1) a method for quickly grouping polygons into nearly coplanar sets, (2) a fast approach for merging coplanar polygon sets and, (3) a simple, robust triangulation method for polygons created by 1 and 2. The central idea of the algorithm is the notion of treating polygonal data as a collection of segments and removing redundant segments to quickly form polygon hulls which represent the merged coplanar sets.

N-dimensional Topological Nonmetals (TNM) such as N = 2D HgTe/CdTe quantum wells or N = 3D Bi2Se3 have a finite (often tiny) band gap between occupied and unoccupied bands, and show conductive Dirac cones in their N-1 dimensional geometric boundaries. On the other hand, examples of topological semimetals (TSM) are known for 3D solids (Cd3As2) where they have Dirac cones in the 3D system itself. Using density functional calculation of bands and the topological invariant Z2 we predict the existence of 2D topological Dirac semimetal in few monolayers of strain tuned black phosphorus (BP), with Dirac cones induced by band inversion. The band structures of few monolayers and bulk crystal of BP under a few percent biaxial and uniaxial strains were calculated using state-of-art electronic structure methods. The critical strain of the transition to TSM was found to decrease as the layer thickness increases. We will discuss the protection of the Dirac cones by the crystalline symmetry in the 2D TSM and the manipulation of crystalline symmetry, which induces further topological phase transitions. Supported by the NSF-DMREF-13-34170.

A combination of electronic-structure methodologies from density functional theory (DFT) through a tight-binding (TB) model to analytic bond-order potentials (BOPs) has been used to investigate structural trends within TCP phases, which we recently discussed using an empirical structure map [Acta MaterialiaACMAFD1359-645410.1016/j.actamat.2010.10.013 59, 749 (2011)]. First, DFT is used to calculate the structural energy differences across the elemental 4d and 5d transition metal series and the heats of formation of the binary alloys Mo-Re, Mo-Ru, Nb-Re, and Nb-Ru, where we show that the valence electron concentration stabilizes A15, σ, and χ phases but destabilizes μ and Laves phases. Second, a one-parameter canonical d-band TB model in combination with the structural energy difference theorem is found to reproduce the observed elemental DFT structural trends. The structural energy difference theorem is also used to rationalize the influence of the relative size differences on the stability of μ and Laves phases in binary systems. Third, analytic BOP theory using the TB bond integrals as input is shown to converge to the TB structural energy difference curves as the number of moments in the BOP expansion is increased. In order to provide a simple interpretation of these structural energy difference curves in terms of analytic response functions and the differences in the moments of the density of states (DOS), an expression is used for the difference in the band energy that is correct to first order in the Fermi energy differences. We find that the fourth-moment contribution separates the A15, σ, and χ phases from the μ and Laves phases in agreement with the empirical structure map due to difference in the bimodality of the corresponding DOS caused mainly by distortions in their coordination polyhedra from ideal Frank-Kasper polyhedra. Finally, it is shown that at least six moments are needed to predict the structural trend A15→σ→χ.

Topological phase transitions in free fermion systems can be characterized by the closing of single-particle gap and the change in topological invariants. However, in the presence of electronic interactions, topological phase transitions can be more complicated. In paper I of this series [Phys. Rev. B 93, 195163 (2016), 10.1103/PhysRevB.93.195163], we have proposed an efficient scheme to evaluate the topological invariants based on the single-particle Green's function formalism. Here, in paper II, we demonstrate several interaction-driven topological phase transitions (TPTs) in two-dimensional (2D) interacting topological insulators (TIs) via large-scale quantum Monte Carlo (QMC) simulations, based on the scheme of evaluating topological invariants presented in paper I. Across these transitions, the defining symmetries of the TIs have been neither explicitly nor spontaneously broken. In the first two models, the topological invariants calculated from the Green's function formalism succeed in characterizing the topologically distinct phases and identifying interaction-driven TPTs. However, in the other two models, we find that the single-particle gap does not close and the topological invariants constructed from the single-particle Green's function acquire no change across the TPTs. Unexpected breakdown of the Green's function formalism in constructing the topological invariants is thus discovered. We thence classify the topological phase transitions in interacting TIs into two categories in practical computation: Those that have noninteracting correspondence can be characterized successfully by the topological invariants constructed from the Green's functions, while for the others that do not have noninteracting correspondence, the Green's function formalism experiences a breakdown, but more interesting and exciting phenomena, such as emergent collective critical modes at the transition, arise. Discussion on the success and breakdown of topological invariants

The manipulation of acoustic wave propagation in fluids has numerous applications, including some in everyday life. Acoustic technologies frequently develop in tandem with optics, using shared concepts such as waveguiding and metamedia. It is thus noteworthy that an entirely novel class of electromagnetic waves, known as "topological edge states," has recently been demonstrated. These are inspired by the electronic edge states occurring in topological insulators, and possess a striking and technologically promising property: the ability to travel in a single direction along a surface without backscattering, regardless of the existence of defects or disorder. Here, we develop an analogous theory of topological fluid acoustics, and propose a scheme for realizing topological edge states in an acoustic structure containing circulating fluids. The phenomenon of disorder-free one-way sound propagation, which does not occur in ordinary acoustic devices, may have novel applications for acoustic isolators, modulators, and transducers.

The manipulation of acoustic wave propagation in fluids has numerous applications, including some in everyday life. Acoustic technologies frequently develop in tandem with optics, using shared concepts such as waveguiding and metamedia. It is thus noteworthy that an entirely novel class of electromagnetic waves, known as "topological edge states," has recently been demonstrated. These are inspired by the electronic edge states occurring in topological insulators, and possess a striking and technologically promising property: the ability to travel in a single direction along a surface without backscattering, regardless of the existence of defects or disorder. Here, we develop an analogous theory of topological fluid acoustics, and propose a scheme for realizing topological edge states in an acoustic structure containing circulating fluids. The phenomenon of disorder-free one-way sound propagation, which does not occur in ordinary acoustic devices, may have novel applications for acoustic isolators, modulators, and transducers. PMID:25839273

Smoke, fog, jelly, paints, milk and shaving cream are common everyday examples of colloids, a type of soft matter consisting of tiny particles dispersed in chemically distinct host media. Being abundant in nature, colloids also find increasingly important applications in science and technology, ranging from direct probing of kinetics in crystals and glasses to fabrication of third-generation quantum-dot solar cells. Because naturally occurring colloids have a shape that is typically determined by minimization of interfacial tension (for example, during phase separation) or faceted crystal growth, their surfaces tend to have minimum-area spherical or topologically equivalent shapes such as prisms and irregular grains (all continuously deformable--homeomorphic--to spheres). Although toroidal DNA condensates and vesicles with different numbers of handles can exist and soft matter defects can be shaped as rings and knots, the role of particle topology in colloidal systems remains unexplored. Here we fabricate and study colloidal particles with different numbers of handles and genus g ranging from 1 to 5. When introduced into a nematic liquid crystal--a fluid made of rod-like molecules that spontaneously align along the so-called 'director'--these particles induce three-dimensional director fields and topological defects dictated by colloidal topology. Whereas electric fields, photothermal melting and laser tweezing cause transformations between configurations of particle-induced structures, three-dimensional nonlinear optical imaging reveals that topological charge is conserved and that the total charge of particle-induced defects always obeys predictions of the Gauss-Bonnet and Poincaré-Hopf index theorems. This allows us to establish and experimentally test the procedure for assignment and summation of topological charges in three-dimensional director fields. Our findings lay the groundwork for new applications of colloids and liquid crystals that range from

This theme issue on transitions for individuals with disabilities contains nine papers discussing transition programs and issues. "Transition Issues for the 1990s," by Michael J. Ward and William D. Halloran, discusses self-determination, school responsibility for transition, continued educational engagement of at-risk students, and service…

Quasiparticle poisoning and diabatic transitions may significantly narrow the window for the experimental observation of the 4 π -periodic dc Josephson effect predicted for topological Josephson junctions. Here, we show that switching-current measurements provide accessible and robust signatures for topological superconductivity which persist in the presence of quasiparticle poisoning processes. Such measurements provide access to the phase-dependent subgap spectrum and Josephson currents of the topological junction when incorporating it into an asymmetric SQUID together with a conventional Josephson junction with large critical current. We also argue that pump-probe experiments with multiple current pulses can be used to measure the quasiparticle poisoning rates of the topological junction. The proposed signatures are particularly robust, even in the presence of Zeeman fields and spin-orbit coupling, when focusing on short Josephson junctions. Finally, we also consider microwave excitations of short topological Josephson junctions which may complement switching-current measurements.

Topological defects play an important role in the melting phenomena in two-dimensions. In this work, we report experimental observation of topological defect induced melting in two-dimensional electron systems (2DES) in the presence of strong Coulomb interaction and disorder. The phenomenon is characterised by measurement of conductivity which goes to zero in a Berezinskii-Kosterlitz-Thouless like transition. Further evidence is provided via low-frequency conductivity noise measurements.

Includes four articles: "Career Aspirations" (Field); "Making the Transition to a New Curriculum" (Baker, Householder); "How about a 'Work to School' Transition?" (Glasberg); and "Technological Improvisation: Bringing CNC to Woodworking" (Charles, McDuffie). (SK)

This "feature issue" focuses on transition from school to adult life for persons with disabilities. Included are "success stories," brief program descriptions, and a list of resources. Individual articles include the following titles and authors: "Transition: An Energizing Concept" (Paul Bates); "Transition Issues for the 1990s" (William Halloran…

In the present paper, we consider effects of quantization in a topos approach of quantum theory. A quantum system is assumed to be coded in a quantum topos, by which we mean the topos of presheaves on the context category of commutative subalgebras of a von Neumann algebra of bounded operators on a Hilbert space. A classical system is modeled by a Lie algebra of classical observables. It is shown that a quantization map from the classical observables to self-adjoint operators on the Hilbert space naturally induces geometric morphisms from presheaf topoi related to the classical system to the quantum topos. By means of the geometric morphisms, we give Lawvere-Tierney topologies on the quantum topos (and their equivalent Grothendieck topologies on the context category). We show that, among them, there exists a canonical one which we call a quantization topology. We furthermore give an explicit expression of a sheafification functor associated with the quantization topology.

We report the characterization of the misfit compound (Pb1-xSnxSe2)1.16(TiSe2)2 for 0 ≤ x ≤ 0.6, in which a [100] rocksalt-structure bilayer of Pb1-xSnxSe, which is a topological crystalline insulator in bulk form, alternates with a double layer of the normally non-superconducting transition metal dichalcogenide TiSe2. The x dependence of Tc displays a weak dome-like shape with a maximum Tc of 4.5 K at x = 0.2; there is only a subtle change in Tc at the composition where the trivial to topologicaltransition occurs in bulk Pb1-xSnxSe. We present the characterization of the superconductor at x = 0.4, for which the bulk Pb1-xSnxSe phase is in the topological crystalline insulator regime. For this material, the Sommerfeld parameter γ = 11.06 mJ mol-1 K-2, the Debye temperature ΘD = 161 K, the normalized specific heat jump value ΔC/γTc = 1.38 and the electron-phonon constant value λep = 0.72, suggesting that (Pb0.6Sn0.4Se)1.16(TiSe2)2 is a BCS-type weak coupling superconductor. This material may be of interest for probing the interaction of superconductivity with the surface states of a topological crystalline insulator.

We report the characterization of the misfit compound (Pb1-xSnxSe2)1.16(TiSe2)2 for 0 ≤ x ≤ 0.6, in which a [100] rocksalt-structure bilayer of Pb1-xSnxSe, which is a topological crystalline insulator in bulk form, alternates with a double layer of the normally nonsuperconducting transition metal dichalcogenide TiSe2. The x dependence of Tc displays a weak dome-like shape with a maximum Tc of 4.5 K at x = 0.2; there is only a subtle change in Tc at the composition where the trivial to topologicaltransition occurs in bulk Pb1-xSnxSe. We present the characterization of the superconductor at x = 0.4, for whichmore » the bulk Pb1-xSnxSe phase is in the topological crystalline insulator regime. For this material, the Sommerfeld parameter γ = 11.06 mJ mol-1 K-2, the Debye temperature ΘD = 161 K, the normalized specific heat jump value ΔC/γTc = 1.38 and the electron-phonon constant value γep = 0.72, suggesting that (Pb0.6Sn0.4Se)1.16(TiSe2)2 is a BCS-type weak coupling superconductor. This material may be of interest for probing the interaction of superconductivity with the surface states of a topological crystalline insulator.« less

Cooperative phenomena in complex networks are expected to display unusual characteristics, associated with the peculiar topology of these systems. In this context we study networks of interacting stochastic two-state units as a model of cooperative decision making. Each unit in isolation generates a Poisson process with rate g. We show that when the cooperation is introduced, the decision-making process becomes intermittent. The decision-time distribution density characterized by inverse power-law behavior is defined as a dynamic complexity. Further, the onset of intermittency, expressed in terms of the coupling parameter K, is used as a measure of dynamic efficiency of investigated topologies. We find that the dynamic complexity emerges from regular and small-world topologies. In contrast, both random and scale-free networks correspond to fast transition into exponential decision-time distribution. This property is accompanied by high dynamic efficiency of the decision-making process. Our results indicate that complex dynamical processes occurring on networks could be related to relatively simple topologies.

In steels and single-crystal superalloys the control of the formation of topologically close-packed (TCP) phases is critical for the performance of the material. The structural stability of TCP phases in multi-component transition-metal alloys may be rationalized in terms of the average valence-electron count \\bar {N} and the composition-dependent relative volume-difference \\overline {\\Delta V/V} . We elucidate the interplay of these factors by comparing density-functional theory calculations to an empirical structure map based on experimental data. In particular, we calculate the heat of formation for the TCP phases A15, C14, C15, C36, χ, μ and σ for all possible binary occupations of the Wyckoff positions. We discuss the isovalent systems V/Nb-Ta to highlight the role of atomic-size difference and observe the expected stabilization of C14/C15/C36/μ by \\overline {\\Delta V/V} at ΔN = 0 in V-Ta. In the systems V/Nb-Re, we focus on the well-known trend of A15 → σ → χ stability with increasing \\bar {N} and show that the influence of \\overline {\\Delta V/V} is too weak to stabilize C14/C15/C36/μ in Nb-Re. As an example for a significant influence of both \\bar {N} and \\overline {\\Delta V/V} , we also consider the systems Cr/Mo-Co. Here the sequence A15 → σ → χ is observed in both systems but in Mo-Co the large size-mismatch stabilizes C14/C15/C36/μ. We also include V/Nb-Co that cover the entire valence range of TCP stability and also show the stabilization of C14/C15/C36/μ. Moreover, the combination of a large volume-difference with a large mismatch in valence-electron count reduces the stability of the A15/σ/χ phases in Nb-Co as compared to V-Co. By comparison to non-magnetic calculations we also find that magnetism is of minor importance for the structural stability of TCP phases in Cr/Mo-Co and in V/Nb-Co.

A new variety on non-coding RNA has been discovered by several groups: circular RNA (circRNA). This discovery raises intriguing questions about the possibility of the existence of knotted RNA molecules and the existence of a new class of enzymes changing RNA topology, RNA topoisomerases. PMID:23603781

Emergence of the topological invariant and the magnetic moment in topological insulators doped with magnetic impurities is studied based on a mutual cooperation between the spin-orbit coupling of electrons and the spin exchange of these electrons with magnetic impurity moments. The mutual cooperation is realized based on the Kane-Mele model in the presence of magnetic impurities. The topological invariants and the spontaneous magnetization are self-consistently determined within the dynamical mean-field theory. We find different magnetic topological phase transitions, depending on the electron filling. At half filling an antiferromagnetic topological insulator, which exhibits the quantum spin Hall effect, exists in the phase region between the paramagnetic topological insulator and the trivially topological antiferromagnetic insulator. At quarter and three-quarter fillings, a ferromagnetic topological insulator, which exhibits the quantum anomalous Hall effect, occurs in the strong spin-exchange regime.

Our goal is autonomous real-time control of a mobile robot. In this paper we want to show a possibility to learn topological maps of a large-scale indoor environment autonomously. In the literature there are two paradigms how to store information on the environment of a robot: as a grid-based (geometric) or as a topological map. While grid-based maps are considerably easy to learn and maintain, topological maps are quite compact and facilitate fast motion-planning.

We develop an approximate theory of phonon-induced topological insulation in Dirac materials. In the weak-coupling regime, long-wavelength phonons may favor topological phases in Dirac insulators with direct and narrow band gaps. This phenomenon originates from electron-phonon matrix elements, which change qualitatively under a band inversion. A similar mechanism applies to weak Coulomb interactions and spin-independent disorder; however, the influence of these on band topology is largely independent of temperature. As applications of the theory, we evaluate the temperature dependence of the critical thickness and the critical stoichiometric ratio for the topologicaltransition in CdTe/HgTe quantum wells and in BiTl(S1-δSeδ)2, respectively.

Applications of the hairy ball theorem to the geometrical optics are discussed. When the ideal mirror, topologically equivalent to a sphere, is illuminated at every point, the "hairy ball theorem" prescribes the existence of at least one point at which the incident light will be normally reflected. For the more general case of the surface, topologically equivalent to a sphere, which is both reflecting and refracting the "hairy ball theorem" predicts the existence of at least one point, at which the incident light will be normally reflected and also normally refracted.

Origami and kirigami have emerged as potential tools for the design of mechanical metamaterials whose properties such as curvature, Poisson ratio, and existence of metastable states can be tuned using purely geometric criteria. A major obstacle to exploiting this property is the scarcity of tools to identify and program the flexibility of fold patterns. We exploit a recent connection between spring networks and quantum topological states to design origami with localized folding motions at boundaries and study them both experimentally and theoretically. These folding motions exist due to an underlying topological invariant rather than a local imbalance between constraints and degrees of freedom. We give a simple example of a quasi-1D folding pattern that realizes such topological states. We also demonstrate how to generalize these topological design principles to two dimensions. A striking consequence is that a domain wall between two topologically distinct, mechanically rigid structures is deformable even when constraints locally match the degrees of freedom. PMID:27081987

Origami and kirigami have emerged as potential tools for the design of mechanical metamaterials whose properties such as curvature, Poisson ratio, and existence of metastable states can be tuned using purely geometric criteria. A major obstacle to exploiting this property is the scarcity of tools to identify and program the flexibility of fold patterns. We exploit a recent connection between spring networks and quantum topological states to design origami with localized folding motions at boundaries and study them both experimentally and theoretically. These folding motions exist due to an underlying topological invariant rather than a local imbalance between constraints and degrees of freedom. We give a simple example of a quasi-1D folding pattern that realizes such topological states. We also demonstrate how to generalize these topological design principles to two dimensions. A striking consequence is that a domain wall between two topologically distinct, mechanically rigid structures is deformable even when constraints locally match the degrees of freedom.

The leaves of vascular plants contain highly complex venation networks consisting of recursively nested, hierarchically organized loops. We analyze the topology of the venation of leaves from ca. 200 species belonging to ca. 10 families, defining topological metrics that quantify the hierarchical nestedness of the network cycles. We find that most of the venation variability can be described by a two dimensional phenotypic space, where one dimension consists of a linear combination of geometrical metrics and the other dimension of topological, previously uncharacterized metrics. We show how this new topological dimension in the phenotypic space significantly improves identification of leaves from fragments, by calculating a ``leaf fingerprint'' from the topology and geometry of the higher order veins. Further, we present a simple model suggesting that the topological phenotypic traits can be explained by noise effects and variations in the timing of higher order vein developmental events. This work opens the path to (a) new quantitative identification techniques for leaves which go beyond simple geometric traits such as vein density and (b) topological quantification of other planar or almost planar networks such as arterial vaculature in the neocortex and lung tissue.

We propose the use of finite topological spaces as examples in a point-set topology class especially suited to help students transition into abstract mathematics. We describe how carefully chosen examples involving finite spaces may be used to reinforce concepts, highlight pathologies, and develop students' non-Euclidean intuition. We end with a…

In order to obtain the energy deposition pattern of ionizing radiation in the nanometric scale of genetic material and to investigate the different sensitivities of the DNA conformations, direct effects of (60)Co gamma rays on the three A, B and Z conformations of DNA have been studied. For this purpose, single-strand breaks (SSB), double-strand breaks (DSB), base damage (BD), hit probabilities and three microdosimetry quantities (imparted energy, mean chord length and lineal energy) in the mentioned DNA conformations have been calculated and compared by using GEometry ANd Tracking 4 (Geant4) toolkit. The results show that A-, B- and Z-DNA conformations have the highest yields of DSB (1.2 Gy(-1) Gbp(-1)), SSB (25.2 Gy(-1) Gbp(-1)) and BD (4.81 Gy(-1) Gbp(-1)), respectively. Based on the investigation of direct effects of radiation, it can be concluded that the DSB yield is largely correlated to the topological characteristics of DNA models, although the SSB yield is not. Moreover, according to the comparative results of the present study, a reliable candidate parameter for describing the relationship between DNA damage yields and geometry of DNA models in the theoretical radiation biology research studies would be the mean chord length (4 V/S) of the models. PMID:26984469

A geometric representation scheme is outlined which utilizes the natural design variable concept. A base configuration with distinct topological features is created. This configuration is then deformed to define components with similar topology but different geometry. The values of the deforming loads are the geometric entities used in the shape representation. The representation can be used for all geometric design studies; it is demonstrated here for structural optimization. This technique can be used in parametric design studies, where the system response is defined as functions of geometric entities. It can also be used in shape optimization, where the geometric entities of an original design are modified to maximize performance and satisfy constraints. Two example problems are provided. A cantilever beam is elongated to meet new design specifications and then optimized to reduce volume and satisfy stress constraints. A similar optimization problem is presented for an automobile crankshaft section. The finite element method is used to perform the analyses.

The cause of a pipe clip during the setting of the pipe is determined on the basis of modeling. The method, which excludes the formation of a defect in a semi finished product by changing the configuration of the setting transition, is developed.

We study topological superconductivity in the spin-orbit coupling nanowire system by using the fidelity approach. The wire is modeled as a one layer lattice chain with Zeeman energy and spin-orbital coupling, which is in proximity to a multi-layer superconductor. In particular, we study the effects of disorders and find that the fidelity susceptibility has multiple peaks. It is revealed that one peak indicates the topological quantum phase transition, while other peaks are signaling the pinning of the Majorana bound states by disorders. Our study shows that fidelity and fidelity susceptibility are very useful to investigate the topological quantum phase transition in superconductors. This work is supported by NSFC-11574404, 11275279, and NBRPC-2012CB821400.

The present study is an extension of our recent study in which we attempted statistical analysis of the data assembly of age-adjusted incidence rates (AAIRs) of a tumor without topological data manipulation for each of 20 individual tumors in scope, for each of 6 cancer registration areas in space, and for a period of early 1960's to mid 1980's in time. This time, a data assembly of log AAIR changes in time and space first passed through the process of topological data manipulation, and then underwent the sequential regression analysis so that we could assess the fitness of log AAIR changes either in space or in time to the equilibrium model of the law of mass action from the viewpoint of the interaction between oncogene activation and tumor suppressor gene inactivation. For the sake of comparison, the fitness of the cancer risk data to the equilibrium model was assessed in the framework of 3 sets of coordinates: a) the original (x org, y org) coordinates in which most of the log AAIR data assemblies in their data variations were classified as the oncogene activation type in the field of centripetal force (r seq=-1.000). b) The rect (X rect, Y rect) coordinates in which the log AAIR data assemblies were very often classified as the tumor suppressor gene inactivation type in the field of centrifugal force (r seq=+1.000). c) The para (X para, Y para) coordinates in which the log AAIR data assemblies were mostly classified as the intermediate type as regards the fitness to the equilibrium model. The rect-coordinates and the para-coordinates, 2 variants of angular rotation of the original coordinates, were so designed as to allow their X-axes to run each at a right angle and parallel to the regression line of the original pair data block. The results obtained were as follows: a) poor fitness of the log AAIR changes in space to the equilibrium model in the rect-coordinates was found in male breast cancer, male thyroid cancer, female esophageal cancer, female laryngeal

Understanding and control of spin degrees of freedom on the surfaces of topological materials are key to future applications as well as for realizing novel physics such as the axion electrodynamics associated with time-reversal (TR) symmetry breaking on the surface. We experimentally demonstrate magnetically induced spin reorientation phenomena simultaneous with a Dirac-metal to gapped-insulator transition on the surfaces of manganese-doped Bi2Se3 thin films. The resulting electronic groundstate exhibits unique hedgehog-like spin textures at low energies, which directly demonstrate the mechanics of TR symmetry breaking on the surface. We further show that an insulating gap induced by quantum tunnelling between surfaces exhibits spin texture modulation at low energies but respects TR invariance. These spin phenomena and the control of their Fermi surface geometrical phase first demonstrated in our experiments pave the way for the future realization of many predicted exotic magnetic phenomena of topological origin.

We present a class of mechanical metamaterials characterized by a uniform soft deformation--a large, zero-energy homogeneous elastic deformation mode of the structure--that may be used to induce topologicaltransitions and dramatically change mechanical and acoustic properties of the structure. We show that the existence of such a mode determines certain exotic mechanical and acoustic properties of the structure and its activation can reversibly alter and tune these properties. This serves as the basis for a design principle for mechanical metamaterials with tunable properties. When the structure's uniform mode is primarily dilational (shearing) its surface (bulk) possesses phonon modes with vanishing speed of sound. Maxwell lattices comprise a subclass of such material which, owing to their critical coordination number (four, in 2D), necessarily possess such a uniform zero mode, often termed a Guest mode, and which may be topologically polarized, such that zero modes are moved from one edge to another. We show that activating the deformation can alter the shear/dilational character of the mode and topologically polarize the structure, thereby altering the bulk and surface properties at no significant energy cost. arXiv:1510.06389 [cond-mat.soft] NWO, Delta Institute of Physics, ICAM fellowship (DZR) and NSF Grant PHY-1402971 at University of Michigan (KS).

We propose a new type of interferometry, based on geometric phases accumulated by a periodically driven two-level system undergoing multiple Landau-Zener transitions. As a specific example, we study its implementation in a superconducting charge pump. We find that interference patterns appear as a function of the pumping frequency and the phase bias, and clearly manifest themselves in the pumped charge. We also show that the effects described should persist in the presence of realistic decoherence. PMID:22181761

Pierre M. Van Hiele created five levels of geometric thinking. We decided to identify the level of geometric thinking in the students in Slovenia, aged 9 to 11 years. The majority of students (60.7%) are at the transition between the zero (visual) level and the first (descriptive) level of geometric thinking. Nearly a third (31.7%) of students is…

Inverse problems can be defined as the area of mathematics that attempts to reconstruct a physical or mathematical object from derived data. Frequently, this means the evaluation of parameters or other numerical quantities (such as eigenvalues) that characterize or provide information about the system. There are, however, other aspects of a system that are important, but are not as readily summarized by numerical quantities. If one considers observations of diabetic patients (using metabolic quantities), one will find that the data breaks up into components, or pieces, corresponding to distinct forms of the disease. The decomposition of data sets into disjoint pieces, or clustering, is an aspect of the study of the shape of the data, albeit one that has been extensively studied. A more complex notion of shape appears in observations of a predator-prey system governed by a Lotka-Volterra equation. One would find that exact observations, consisting of (prey population, predator population) pairs, appear to lie along a simple closed curve in the plane. The fact that the data lies along such a closed curve is an important piece of information, since it suggests that the system displays recurrent behavior. If one did not know, a priori, that the system is governed by a Lotka-Volterra equation, then it would not be immediately obvious that the system is undergoing recurrent motion, and this deduction would constitute a significant insight. In this case, it is again the shape of the data, namely the fact that it lies on a simple closed curve, which is the key insight. Shape is a somewhat nebulous concept, which at first blush may be too intuitive to make precise mathematically, and describe quantitatively. Within pure mathematics, the disciplines of topology and differential geometry are designed exactly to address this problem. They provide explicit signatures which, in precise senses, quantify and describe the shape of a geometric object. In addition, they provide

Inverse problems can be defined as the area of mathematics that attempts to reconstruct a physical or mathematical object from derived data. Frequently, this means the evaluation of parameters or other numerical quantities (such as eigenvalues) that characterize or provide information about the system. There are, however, other aspects of a system that are important, but are not as readily summarized by numerical quantities. If one considers observations of diabetic patients (using metabolic quantities), one will find that the data breaks up into components, or pieces, corresponding to distinct forms of the disease. The decomposition of data sets into disjoint pieces, or clustering, is an aspect of the study of the shape of the data, albeit one that has been extensively studied. A more complex notion of shape appears in observations of a predator-prey system governed by a Lotka-Volterra equation. One would find that exact observations, consisting of (prey population, predator population) pairs, appear to lie along a simple closed curve in the plane. The fact that the data lies along such a closed curve is an important piece of information, since it suggests that the system displays recurrent behavior. If one did not know, a priori, that the system is governed by a Lotka-Volterra equation, then it would not be immediately obvious that the system is undergoing recurrent motion, and this deduction would constitute a significant insight. In this case, it is again the shape of the data, namely the fact that it lies on a simple closed curve, which is the key insight. Shape is a somewhat nebulous concept, which at first blush may be too intuitive to make precise mathematically, and describe quantitatively. Within pure mathematics, the disciplines of topology and differential geometry are designed exactly to address this problem. They provide explicit signatures which, in precise senses, quantify and describe the shape of a geometric object. In addition, they provide

We predict the existence of a topological superradiant state in a two-component degenerate Fermi gas in a cavity. The superradiant light generation in the transversely driven cavity mode induces a cavity-assisted spin-orbit coupling in the system and opens a bulk gap at half filling. This mechanism can simultaneously drive a topological phase transition in the system, yielding a topological superradiant state. We map out the steady-state phase diagram of the system in the presence of an effective Zeeman field, and identify a critical tetracritical point beyond which the topological and the conventional superraidiant phase boundaries separate. We propose to detect the topological phase transition based on its signatures in either the momentum distribution of the atoms or in the cavity photon occupation.

Topological numbers can characterize the transition between different topological phases, which are not described by Landau's paradigm of symmetry breaking. Since the discovery of the quantum Hall effect, more topological phases have been theoretically predicted and experimentally verified. However, it is still an experimental challenge to directly measure the topological numbers of various predicted topological phases. In this Letter, we demonstrate quantum simulation of topological phase transition of a quantum wire (QW), by precisely modulating the Hamiltonian of a single nitrogen-vacancy (NV) center in diamond. Deploying a quantum algorithm of finding eigenvalues, we reliably extract both the dispersion relations and topological numbers. This method can be further generalized to simulate more complicated topological systems. PMID:27541449

Topological numbers can characterize the transition between different topological phases, which are not described by Landau's paradigm of symmetry breaking. Since the discovery of the quantum Hall effect, more topological phases have been theoretically predicted and experimentally verified. However, it is still an experimental challenge to directly measure the topological numbers of various predicted topological phases. In this Letter, we demonstrate quantum simulation of topological phase transition of a quantum wire (QW), by precisely modulating the Hamiltonian of a single nitrogen-vacancy (NV) center in diamond. Deploying a quantum algorithm of finding eigenvalues, we reliably extract both the dispersion relations and topological numbers. This method can be further generalized to simulate more complicated topological systems.

If the Universe undergoes a phase transition, at which global monopoles are created or destroyed, topology of its spatial sections can change. More specifically, by making use of Myers' theorem, we show that, after a transition in which global monopoles form, spatial sections of a spatially flat, infinite Universe becomes finite and closed. This implies that global monopoles can change the topology of Universe's spatial sections (from infinite and open to finite and closed). Global monopoles cannot alter the topology of the space-time manifold.

Networks are topological and geometric structures used to describe systems as different as the Internet, the brain, or the quantum structure of space-time. Here we define complex quantum network geometries, describing the underlying structure of growing simplicial 2-complexes, i.e., simplicial complexes formed by triangles. These networks are geometric networks with energies of the links that grow according to a nonequilibrium dynamics. The evolution in time of the geometric networks is a classical evolution describing a given path of a path integral defining the evolution of quantum network states. The quantum network states are characterized by quantum occupation numbers that can be mapped, respectively, to the nodes, links, and triangles incident to each link of the network. We call the geometric networks describing the evolution of quantum network states the quantum geometric networks. The quantum geometric networks have many properties common to complex networks, including small-world property, high clustering coefficient, high modularity, and scale-free degree distribution. Moreover, they can be distinguished between the Fermi-Dirac network and the Bose-Einstein network obeying, respectively, the Fermi-Dirac and Bose-Einstein statistics. We show that these networks can undergo structural phase transitions where the geometrical properties of the networks change drastically. Finally, we comment on the relation between quantum complex network geometries, spin networks, and triangulations.

In quantum mechanics, the path-dependent geometrical phase associated with a physical system, over and above the familiar dynamical phase, was initially discovered in the context of adiabatically changing environments. Subsequently, Aharonov and Anandan liberated this phase from the original formulation of Berry, which used Hamiltonians, dependent on curves in a classical parameter space, to represent the cyclic variations of the environments. Their purely quantum mechanical treatment, independent of Hamiltonians, instead used the non-trivial topological structure of the projective space of one-dimensional subspaces of an appropriate Hilbert space. The geometrical phase, in their treatment, results from a parallel transport of the time-dependent pure quantum states along a curve in this space, which is endowed with an abelian connection. Unlike Berry, they were able to achieve this without resort to an adiabatic approximation or to a time-independent eigenvalue equation. Prima facie, these two approaches are conceptually quite different. After a review of both approaches, an exposition bridging this apparent conceptual gap is given; by rigorously analyzing a model composite system, it is shown that, in an appropriate correspondence limit, the Berry phase can be recovered as a special case from the Aharonov-Anandan phase. Moreover, the model composite system is used to show that Berry's correction to the traditional Born-Oppenheimer energy spectra indeed brings the spectra closer to the exact results. Then, an experimental arrangement to measure geometrical phases associated with cyclic and non-cyclic variations of quantum states of an entangled composite system is proposed, utilizing the fundamental ideas of the recently opened field of two-particle interferometry. This arrangement not only resolves the controversy regarding the true nature of the phases associated with photon states, but also unequivocally predicts experimentally accessible geometrical phases in a

Geometrictopology and structural crystallography concepts are combined to define a new area we call Structural Crystallographic Topology, which may be of interest to both crystallographers and mathematicians. In this paper, we represent crystallographic symmetry groups by orbifolds and crystal structures by Morse - functions. The Morse function uses mildly overlapping Gaussian thermal-motion probability density functions centered on atomic sites to form a critical net with peak, pass, pale, and pit critical points joined into a graph by density gradient-flow separatrices. Critical net crystal structure drawings can be made with the ORTEP-III graphics pro- An orbifold consists of an underlying topological space with an embedded singular set that represents the Wyckoff sites of the crystallographic group. An orbifold for a point group, plane group, or space group is derived by gluing together equivalent edges or faces of a crystallographic asymmetric unit. The critical-net-on-orbifold model incorporates the classical invariant lattice complexes of crystallography and allows concise quotient-space topological illustrations to be drawn without the repetition that is characteristic of normal crystal structure drawings.

We realized a quantum geometric "charge" pump for a Bose-Einstein condensate (BEC) in the lowest Bloch band of a novel bipartite magnetic lattice. Topological charge pumps in filled bands yield quantized pumping set by the global—topological—properties of the bands. In contrast, our geometric charge pump for a BEC occupying just a single crystal momentum state exhibits nonquantized charge pumping set by local—geometrical—properties of the band structure. Like topological charge pumps, for each pump cycle we observed an overall displacement (here, not quantized) and a temporal modulation of the atomic wave packet's position in each unit cell, i.e., the polarization.

The original Self-Organizing Feature Map (SOFM) has been extended in many ways to suit different goals and application domains. However, the topologies of the map lattice that we can found in literature are nearly always square or, more rarely, hexagonal. In this paper we study alternative grid topologies, which are derived from the geometrical theory of tessellations. Experimental results are presented for unsupervised clustering, color image segmentation and classification tasks, which show that the differences among the topologies are statistically significant in most cases, and that the optimal topology depends on the problem at hand. A theoretical interpretation of these results is also developed. PMID:24861385

A variety of scenarios are considered which shed light upon the uses and limitations of classical geometric and topological notions in string theory. The primary focus is on situations in which D-brane or string probes of a given classical space-time see the geometry quite differently than one might naively expect. In particular, situations in which extra dimensions, non-commutative geometries as well as other non-local structures emerge are explored in detail. Further, a preliminary exploration of such issues in Lorentzian space-times with non-trivial causal structures within string theory is initiated.

The possibility of realizing topological insulators by the spontaneous formation of electronic superstructures is theoretically investigated in a minimal two-orbital model including both the spin-orbit coupling and electron correlations on a triangular lattice. Using the mean-field approximation, we show that the model exhibits several different types of charge-ordered insulators, where the charge disproportionation forms a honeycomb or kagome superstructure. We find that the charge-ordered insulators in the presence of strong spin-orbit coupling can be topological insulators showing quantized spin Hall conductivity. Their band gap is dependent on electron correlations as well as the spin-orbit coupling, and even vanishes while showing the massless Dirac dispersion at the transition to a trivial charge-ordered insulator. Our results suggest a new route to realize and control topological states of quantum matter by the interplay between the spin-orbit coupling and electron correlations.

Over the past few years the experimental research on three-dimensional topological insulators have emerged as one of the most rapidly developing fields in condensed matter physics. In this talk, we report on two new developments in the field: The first part is on the dynamic interplay between ferromagnetism and the Z2 topological insulator state (leading to a magnetic topological insulator). We present our spin-resolved photoemission and magnetic dichroic experiments on MBE grown films where a hedgehog-like spin texture is revealed on the magnetically ordered surface of Mn-Bi2Se3 revealing a Berry's phase gradient in energy-momentum space of the crystal. A chemically/electrically tunable Berry's phase switch is further demonstrated via the tuning of the spin groundstate in Mn-Bi2Se3 revealed in our data (Nature Physics 8, 616 (2012)). The second part of this talk describes our experimental observation of a new topological phase of matter, namely a topological crystalline insulator where space group symmetries replace the role of time-reversal symmetry in an otherwise Z2 topological insulator predicted in theory. We experimentally investigate the possibility of a mirror symmetry protected topological phase transition in the Pb1-xSnxTe alloy system, which has long been known to contain an even number of band inversions based on band theory. Our experimental results show that at a composition below the theoretically predicted band inversion, the system is fully gapped, whereas in the band-inverted regime, the surface exhibits even number of spin-polarized Dirac cone states revealing mirror-protected topological order (Nature Communications 3, 1192 (2012)) distinct from that observed in Z2 topological insulators. We discuss future experimental possibilities opened up by these new developments in topological insulators research. This work is in collaboration with M. Neupane, C. Liu, N. Alidoust, I. Belopolski, D. Qian, D.M. Zhang, A. Richardella, A. Marcinkova, Q

In this work, we compare two global approaches which are usually considered as completely unconnected one with the other. The former is Thom's topology and the latter is Jung's psychology. More precisely, it seemed to us interesting to adapt some morphologies of Thom's catastrophe theory to some Jung's notions. Thus, we showed that the swallowtail, which is one of these morphologies, was able to describe geometrically the structural organisation of the psyche according to Jung, with its collective unconscious, personal unconscious and conscious. Moreover, we have correlated this morphology with Jung's evolutive processes like individualization and individuation. These comparisons incited us to think that some morphologies of Thom's catastrophe theory are the geometrical dealing of Jung's archetypes. PMID:20658172

One intriguing aspect of martian impact crater morphology is the change of crater cavity and ejecta characteristics from the mid-latitudes to the polar regions. This is thought to reflect differences in target properties such as an increasing presence of ice in the polar regions. Previous image-based efforts concerning martian crater morphology has documented some aspects of this, but has been hampered by the lack of adequate topography data. Recent Mars Orbiter Laser Altimeter (MOLA) topographic profiles provide a quantitative perspective for interpreting the detailed morphologies of martian crater cavities and ejecta morphology. This study is a preliminary effort to quantify the latitude-dependent differences in morphology with the goal of identifying target-dependent and crater modification effects from the combined of images and MOLA topography. We combine the available MOLA profiles and the corresponding Viking Mars Digital Image Mosaics (MDIMS), and high resolution Viking Orbiter images to focus on two transitional craters; one on the mid-latitudes, and one in the North Polar region. One MOLA pass (MGS Orbit 34) traverses the center of a 15.9 km diameter fresh complex crater located at 12.8degN 83.8degE on the Hesperian ridge plains unit (Hvr). Viking images, as well as MOLA data, show that this crater has well developed wall terraces and a central peak with 429 m of relative relief. Three MOLA passes have been acquired for a second impact crater, which is located at 69.5degN 41degE on the Vastitas Borealis Formation. This fresh rampart crater lacks terraces and central peak structures and it has a depth af 579 m. Correlation between images and MOLA topographic profiles allows us to construct basic facies maps of the craters. Eight main units were identified, four of which are common on both craters.

Topological properties of electronic materials with gapless band structure such as Topological Semimetals(TSMs) and Topological Metals(TMs) have drew lots of attention to both theoretical and experimental physicists recently. Although theoretical prediction of TSMs and TMs have been done well, experimental study of them is quite difficult to perform due to the fact that it is very difficult to control and design certain electronic materials. However, since the topological properties stem from the geometric feature, we can study them in Photonic Crystals(PhCs) which are much easy to be controlled and designed. Here we study 2-dimension PhCs consisting of gyrotropic materials with hexagonal structure. In the Brillouin corner, the dispersion relation has gapless points which are similar to Dirac Cones in electronic materials. We firstly derive the effective Hamiltonian of this system and show that if certain perturbation is added to this effective Hamiltonian, this system belongs to AII class according to Altland and Zirbauer topological classification and is described by a Z2 topological charge. Finally we also propose a way to detect this Z2 topological charge using momentum space Aharonov-Bohm interferometer which is firstly proposed by L.Duca and T.Li,etc.

Topological defects (TDs) appear almost unavoidably in continuous symmetry breaking phase transitions. The topological origin makes their key features independent of systems’ microscopic details; therefore TDs display many universalities. Because of their strong impact on numerous material properties and their significant role in several technological applications it is of strong interest to find simple and robust mechanisms controlling the positioning and local number of TDs. We present a numerical study of TDs within effectively two dimensional closed soft films exhibiting in-plane orientational ordering. Popular examples of such class of systems are liquid crystalline shells and various biological membranes. We introduce the Effective Topological Charge Cancellation mechanism controlling localised positional assembling tendency of TDs and the formation of pairs {defect, antidefect} on curved surfaces and/or presence of relevant “impurities” (e.g. nanoparticles). For this purpose, we define an effective topological charge Δmeff consisting of real, virtual and smeared curvature topological charges within a surface patch Δς identified by the typical spatially averaged local Gaussian curvature K. We demonstrate a strong tendency enforcing Δmeff → 0 on surfaces composed of Δς exhibiting significantly different values of spatially averaged K. For Δmeff ≠ 0 we estimate a critical depinning threshold to form pairs {defect, antidefect} using the electrostatic analogy.

Topological defects (TDs) appear almost unavoidably in continuous symmetry breaking phase transitions. The topological origin makes their key features independent of systems’ microscopic details; therefore TDs display many universalities. Because of their strong impact on numerous material properties and their significant role in several technological applications it is of strong interest to find simple and robust mechanisms controlling the positioning and local number of TDs. We present a numerical study of TDs within effectively two dimensional closed soft films exhibiting in-plane orientational ordering. Popular examples of such class of systems are liquid crystalline shells and various biological membranes. We introduce the Effective Topological Charge Cancellation mechanism controlling localised positional assembling tendency of TDs and the formation of pairs {defect, antidefect} on curved surfaces and/or presence of relevant “impurities” (e.g. nanoparticles). For this purpose, we define an effective topological charge Δmeff consisting of real, virtual and smeared curvature topological charges within a surface patch Δς identified by the typical spatially averaged local Gaussian curvature K. We demonstrate a strong tendency enforcing Δmeff → 0 on surfaces composed of Δς exhibiting significantly different values of spatially averaged K. For Δmeff ≠ 0 we estimate a critical depinning threshold to form pairs {defect, antidefect} using the electrostatic analogy. PMID:27250777

Topological defects (TDs) appear almost unavoidably in continuous symmetry breaking phase transitions. The topological origin makes their key features independent of systems' microscopic details; therefore TDs display many universalities. Because of their strong impact on numerous material properties and their significant role in several technological applications it is of strong interest to find simple and robust mechanisms controlling the positioning and local number of TDs. We present a numerical study of TDs within effectively two dimensional closed soft films exhibiting in-plane orientational ordering. Popular examples of such class of systems are liquid crystalline shells and various biological membranes. We introduce the Effective Topological Charge Cancellation mechanism controlling localised positional assembling tendency of TDs and the formation of pairs {defect, antidefect} on curved surfaces and/or presence of relevant "impurities" (e.g. nanoparticles). For this purpose, we define an effective topological charge Δmeff consisting of real, virtual and smeared curvature topological charges within a surface patch Δς identified by the typical spatially averaged local Gaussian curvature K. We demonstrate a strong tendency enforcing Δmeff → 0 on surfaces composed of Δς exhibiting significantly different values of spatially averaged K. For Δmeff ≠ 0 we estimate a critical depinning threshold to form pairs {defect, antidefect} using the electrostatic analogy. PMID:27250777

In this work, we introduce persistent homology for the analysis of cryo-electron microscopy (cryo-EM) density maps. We identify the topological fingerprint or topological signature of noise, which is widespread in cryo-EM data. For low signal-to-noise ratio (SNR) volumetric data, intrinsic topological features of biomolecular structures are indistinguishable from noise. To remove noise, we employ geometric flows that are found to preserve the intrinsic topological fingerprints of cryo-EM structures and diminish the topological signature of noise. In particular, persistent homology enables us to visualize the gradual separation of the topological fingerprints of cryo-EM structures from those of noise during the denoising process, which gives rise to a practical procedure for prescribing a noise threshold to extract cryo-EM structure information from noise contaminated data after certain iterations of the geometric flow equation. To further demonstrate the utility of persistent homology for cryo-EM data analysis, we consider a microtubule intermediate structure Electron Microscopy Data (EMD 1129). Three helix models, an alpha-tubulin monomer model, an alpha-tubulin and beta-tubulin model, and an alpha-tubulin and beta-tubulin dimer model, are constructed to fit the cryo-EM data. The least square fitting leads to similarly high correlation coefficients, which indicates that structure determination via optimization is an ill-posed inverse problem. However, these models have dramatically different topological fingerprints. Especially, linkages or connectivities that discriminate one model from another, play little role in the traditional density fitting or optimization but are very sensitive and crucial to topological fingerprints. The intrinsic topological features of the microtubule data are identified after topological denoising. By a comparison of the topological fingerprints of the original data and those of three models, we found that the third model is

The static and dynamic properties of ring polymers in concentrated solutions remains one of the last deep unsolved questions in polymer physics. At the same time, the nature of the glass transition in polymeric systems is also not well understood. In this work, we study a novel glass transition in systems made of circular polymers by exploiting the topological constraints that are conjectured to populate concentrated solutions of rings. We show that such rings strongly interpenetrate through one another, generating an extensive network of topological interactions that dramatically affects their dynamics. We show that a kinetically arrested state can be induced by randomly pinning a small fraction of the rings. This occurs well above the classical glass transition temperature at which microscopic mobility is lost. Our work both demonstrates the existence of long-lived inter-ring penetrations and realizes a novel, topologically induced, glass transition. PMID:27118847

The static and dynamic properties of ring polymers in concentrated solutions remains one of the last deep unsolved questions in polymer physics. At the same time, the nature of the glass transition in polymeric systems is also not well understood. In this work, we study a novel glass transition in systems made of circular polymers by exploiting the topological constraints that are conjectured to populate concentrated solutions of rings. We show that such rings strongly interpenetrate through one another, generating an extensive network of topological interactions that dramatically affects their dynamics. We show that a kinetically arrested state can be induced by randomly pinning a small fraction of the rings. This occurs well above the classical glass transition temperature at which microscopic mobility is lost. Our work both demonstrates the existence of long-lived inter-ring penetrations and realizes a novel, topologically induced, glass transition.

We propose a class of photonic Floquet topological insulators based on staggered helical lattices and an efficient numerical method for calculating their Floquet band structure. The lattices support anomalous Floquet topological insulator phases with vanishing Chern number and tunable topologicaltransitions. At the critical point of the topologicaltransition, the band structure hosts a single unpaired Dirac cone, which yields a variety of unusual transport effects: a discrete analogue of conical diffraction, weak antilocalization not limited by intervalley scattering, and suppression of Anderson localization. Unlike previous designs, the effective gauge field strength can be controlled via lattice parameters such as the interhelix distance, significantly reducing radiative losses and enabling applications such as switchable topological waveguiding.

We employ two complementary theoretical approaches to explore the feasibility of altering the topological properties of two-dimensional Rashba spin-orbit coupled superconductors by proper introduction of magnetic disorders. First, using the self-consistent Born approximation, we show that a topologically trivial superconductor can be driven into a chiral topological superconductor upon diluted doping of isolated magnetic disorders, which gradually narrow, close, and reopen the quasi-particle gap of the paired electrons in a nontrivial manner. Such a topological phase transition is further characterized by the change in the corresponding topological invariant. The central predictions made here are then confirmed using the complementary numerical approach by solving the Bogoliubov-de Gennes equations self-consistently within a tight-binding model. We also discuss the validity of the present model studies in connection with existing experimental findings. Collectively, the present study offers appealing new schemes for potential experimental realization of topological superconductors. Supported by NSF of China.

Recent interest in topological superconductivity is based primarily on exploiting proximity effects to obtain this important phase. However, in cold gases it is possible to contemplate ``intrinsic'' topological superfluidity produced with a synthetic spin-orbit coupling and Zeeman field. It is important for such future experiments to establish how low in temperature one needs to go to reach the ordered phase. Similarly, it will be helpful to have a probe of the normal (pseudogap) phase to determine if the ultimate superfluid order will be topological or trivial. In this talk, we address these issues by considering fluctuation effects in such a superfluid, and calculate the critical transition temperature and response functions. We see qualitative signatures of topological superfluidity in spin and charge response functions. We also explore the suppression of superfluidity due to fluctuations, and importantly find that the temperature scales necessary to reach topological superfluidity are reasonably accessible

We show that in crystalline insulators, space group symmetry alone gives rise to a topological classification based on the discretization of electric polarization. Using C3 rotational symmetry as an example, we first prove that the polarization is discretized into three distinct classes, i.e., it can only take three inequivalent values. We then prove that these classes are topologically distinct. Therefore, a Z3 topological classification exists, with polarization as a topological class index. A concrete tight-binding model is derived to demonstrate the Z3 topological phase transition. Using first-principles calculations, we identify graphene on a BN substrate as a possible candidate to realize these Z3 topological states. To complete our analysis, we extend the classification of band structures to all 17 two-dimensional space groups. This work will contribute to a complete theory of symmetry-conserved topological phases and also elucidate topological properties of graphenelike systems.

The Berry phase has found applications in building topological order parameters for certain condensed matter systems. The question whether some geometric phase for mixed states can serve the same purpose has been raised, and proposals are on the table. We analyse the intricate behaviour of Uhlmann's geometric phase in the Kitaev chain at finite temperature, and then argue that it captures quite different physics from that intended. We also analyse the behaviour of a geometric phase introduced in the context of interferometry. For the Kitaev chain, this phase closely mirrors that of the Berry phase, and we argue that it merits further investigation. PMID:27091168

The production of topological defects, especially cosmic strings, in extended inflation models was considered. In extended inflation, the Universe passes through a first-order phase transition via bubble percolation, which naturally allows defects to form at the end of inflation. The correlation length, which determines the number density of the defects, is related to the mean size of bubbles when they collide. This mechanism allows a natural combination of inflation and large scale structure via cosmic strings.

Structural optimization is a field of research that has experienced noteworthy growth for many years. Researchers in this area have developed optimization tools to successfully design and model structures, typically minimizing mass while maintaining certain deflection and stress constraints. Numerous optimization studies have been performed to minimize mass, deflection, and stress on a benchmark cantilever truss problem. Predominantly traditional optimization theory is applied to this problem. The cross-sectional area of each member is optimized to minimize the aforementioned objectives. This Technical Publication (TP) presents a structural optimization technique that has been previously applied to compliant mechanism design. This technique demonstrates a method that combines topology optimization, geometric refinement, finite element analysis, and two forms of evolutionary computation: genetic algorithms and differential evolution to successfully optimize a benchmark structural optimization problem. A nontraditional solution to the benchmark problem is presented in this TP, specifically a geometrically refined topological solution. The design process begins with an alternate control mesh formulation, multilevel geometric smoothing operation, and an elastostatic structural analysis. The design process is wrapped in an evolutionary computing optimization toolset.

Referring to the experimental results of high pressure experiments of Léger et al. (1998) we have calculated the energies of all phases observed for CaCl2 within the DFT formalism using the VASP package, and we have retrieved enthalpies and transition pressures. All phases can be considerably compressed or dilated without much change in energy. This energetic "softness" could even be quantified. We classify the high temperature TiO2-type structure and the PbCl2-type one at highest pressures as the energetically "softest" ones and the SrI2-type one as the "hardest". We furthermore discuss the energy density (E/V) of the different phases and redefine it as a fictive cohesive pressure within these structures. Pursuing our earlier approaches we have analysed the charges of the atoms in the different CaCl2 phases and their change on compression or dilation. On comparing the gradients of the charge curves we define a sort of "charge hardness" which will generally depend on the type of cation-anion pair but also on their topological connection in the respective structures. We speculate that exhausting the "charge softness or hardness" of individual ions in such arrangements may initiate the structural reorganization at the transition pressures.

For inversion-symmetric topological insulators and superconductors characterized by {{{Z}}2} topological invariants, two scaling schemes are proposed to judge topological phase transitions driven by an energy parameter. The scaling schemes renormalize either the phase gradient or the second derivative of the Pfaffian of the time-reversal operator, through which the renormalization group flow of the driving energy parameter can be obtained. The Pfaffian near the time-reversal invariant momentum is revealed to display a universal critical behavior for a great variety of models examined.

The structures of stoichiometric compositions AB, A{sub 2}B, and A{sub 3}B for structures, B19, L1{sub 0}, L1{sub 2}, D0{sub 19}, D0{sub 22}, D0{sub 23}, D0{sub 24}, A15, C14, C15 and C36 have been investigated based on the analysis of diagrams in coordinates of space-filling coefficients Ψ on superstructural compression ΔΩ/Ω. On the basis of the analysis of the abovementioned diagrams, the equation Ψ = f{sub 0}+f{sub 1}(ΔΩ/Ω) has been obtained, and coefficients f{sub 0} and f{sub 1} of the equation for the investigated structures have been determined. It has been established that values of coefficients f{sub 0} and f{sub 1} for Laves phases have higher values than for all other compounds.

We study a Lie algebra of formal vector fields W{sub n} with it application to the perturbative deformed holomorphic symplectic structure in the A-model, and a Calabi-Yau manifold with boundaries in the B-model. We show that equivalent classes of deformations are described by a Hochschild cohomology of the DG-algebra A = (A,Q), Q = {partial_derivative}-bar+{partial_derivative}{sub deform,} which is defined to be the cohomology of (-1){sup n}Q+d{sub Hoch}. Here {partial_derivative}-bar is the initial non-deformed BRST operator while {partial_derivative}{sub deform} is the deformed part whose algebra is a Lie algebra of linear vector fields gl{sub n}.

We study the influence of curvature on the exchange energy of skyrmions and vortices on a paraboloidal surface. It is shown that such structures appear as excitations of the Heisenberg model, presenting topological stability, unlike what happens on other simply-connected geometries such as pseudospheres. We also show that the skyrmion width depends on the geometrical parameters of the paraboloid. The presence of a magnetic field leads to the appearance of 2π-skyrmions, introducing a new characteristic length into the system. Regarding vortices, the geometrical parameters of the paraboloid play an important role in the exchange energy of this excitation.

Motivated by the need for correct and robust 3D models of neuronal processes, we present a method for reconstruction of spatially realistic and topologically correct models from planar cross sections of multiple objects. Previous work in 3D reconstruction from serial contours has focused on reconstructing one object at a time, potentially producing inter-object intersections between slices. We have developed a robust algorithm that removes these intersections using a geometric approach. Our method not only removes intersections but can guarantee a given minimum separation distance between objects. This paper describes the algorithm for geometric adjustment, proves correctness, and presents several results of our high-fidelity modeling. PMID:22003256

When students work with a non-Euclidean distance formula, geometric objects such as circles and segment bisectors can look very different from their Euclidean counterparts. Students and even teachers can experience the thrill of creative discovery when investigating these differences among geometric worlds. In this article, the author describes a…

This paper shows the analysis and design of feedforward neural networks using the coordinate-free system of Clifford or geometric algebra. It is shown that real-, complex-, and quaternion-valued neural networks are simply particular cases of the geometric algebra multidimensional neural networks and that some of them can also be generated using support multivector machines (SMVMs). Particularly, the generation of radial basis function for neurocomputing in geometric algebra is easier using the SMVM, which allows one to find automatically the optimal parameters. The use of support vector machines in the geometric algebra framework expands its sphere of applicability for multidimensional learning. Interesting examples of nonlinear problems show the effect of the use of an adequate Clifford geometric algebra which alleviate the training of neural networks and that of SMVMs. PMID:18249926

Geometric shape and topology of constituent particles can alter many colloidal properties such as Brownian motion, self-assembly, and phase behavior. Thus far, only single-component building blocks of colloids with connected surfaces have been studied, although topological colloids, with constituent particles shaped as freestanding knots and handlebodies of different genus, have been recently introduced. Here we develop a topological class of colloids shaped as multicomponent links. Using two-photon photopolymerization, we fabricate colloidal microparticle analogs of the classic examples of links studied in the field of topology, the Hopf and Solomon links, which we disperse in nematic fluids that possess orientational ordering of anisotropic rod-like molecules. The surfaces of these particles are treated to impose tangential or perpendicular boundary conditions for the alignment of liquid crystal molecules, so that they generate a host of topologically nontrivial field and defect structures in the dispersing nematic medium, resulting in an elastic coupling between the linked constituents. The interplay between the topologies of surfaces of linked colloids and the molecular alignment field of the nematic host reveals that linking of particle rings with perpendicular boundary conditions is commonly accompanied by linking of closed singular defect loops, laying the foundations for fabricating complex composite materials with interlinking-based structural organization. PMID:25825765

Geometric shape and topology of constituent particles can alter many colloidal properties such as Brownian motion, self-assembly, and phase behavior. Thus far, only single-component building blocks of colloids with connected surfaces have been studied, although topological colloids, with constituent particles shaped as freestanding knots and handlebodies of different genus, have been recently introduced. Here we develop a topological class of colloids shaped as multicomponent links. Using two-photon photopolymerization, we fabricate colloidal microparticle analogs of the classic examples of links studied in the field of topology, the Hopf and Solomon links, which we disperse in nematic fluids that possess orientational ordering of anisotropic rod-like molecules. The surfaces of these particles are treated to impose tangential or perpendicular boundary conditions for the alignment of liquid crystal molecules, so that they generate a host of topologically nontrivial field and defect structures in the dispersing nematic medium, resulting in an elastic coupling between the linked constituents. The interplay between the topologies of surfaces of linked colloids and the molecular alignment field of the nematic host reveals that linking of particle rings with perpendicular boundary conditions is commonly accompanied by linking of closed singular defect loops, laying the foundations for fabricating complex composite materials with interlinking-based structural organization. PMID:25825765

Using first-principles calculations, we investigate the band structure evolution and topological phase transitions in TlBiS2 and TlSbS2 under hydrostatic pressure as well as uniaxial and biaxial strain. The phase transitions are identified by parity analysis and by calculating the surface states. Zero, one, and four Dirac cones are found for the (111) surfaces of both TlBiS2 and TlSbS2 when the pressure grows, which confirms trivial-nontrivial-trivial phase transitions. The Dirac cones at the points are anisotropic with large out-of-plane component. TlBiS2 shows normal, topological, and topological crystalline insulator phases under hydrostatic pressure, thus being the first compound to exhibit a phase transition from a topological to a topological crystalline insulator. PMID:25669914

The ground state of the large Hubbard U limit of a honeycomb lattice near half filling is known to be a singlet d +i d -wave superconductor. It is also known that this d +i d superconductor exhibits a chiral p +i p pairing locally at the Dirac cone, characterized by a 2 Z topological invariant. By constructing a dual transformation, we demonstrate that this 2 Z topological superconductor is equivalent to a collection of two topological ferromagnetic insulators. As a result of the duality, the topology of the electronic structures for a d +i d superconductor is controllable via the change of the chemical potential by tuning the gate voltage. In particular, instead of always being a chiral superconductor, we find that the d +i d superconductor undergoes a topological phase transition from a chiral superconductor to a quasihelical superconductor as the gap amplitude or the chemical potential decreases. The quasihelical superconducting phase is found to be characterized by a topological invariant in the pseudospin charge sector with vanishing both the Chern number and the spin Chern number. We further elucidate the topological phase transition by analyzing the relationship between the topological invariant and the rotation symmetry. Due to the angular momentum carried by the gap function and spin-orbit interactions, we show that by placing d +i d superconductors in proximity to ferromagnets, varieties of chiral superconducting phases characterized by higher Chern numbers can be accessed, providing a platform for hosting large numbers of Majorana modes at edges.

We study the phase transition from two different topological phases to the ferromagnetic phase by focusing on points of the phase transition. To this end, we present a detailed mapping from such models to the Ising model in a transverse field. Such a mapping is derived by rewriting the initial Hamiltonian in a new basis so that the final model in such a basis has a well-known approximated phase transition point. Specifically, we consider the toric codes and the color codes on various lattices with Ising perturbation. Our results provide a useful table to compare the robustness of the topological codes and to explicitly show that the robustness of the topological codes depends on triangulation of their underlying lattices.

Plasmons can be supported on graphene sheets as the Dirac electrons oscillate collectively. A tight-binding model for graphene plasmons is a good description as the field confinement in the normal direction is strong. With this model, the topological properties of plasmonic bands in multilayer graphene systems are investigated. The Zak phases of periodic graphene sheet arrays are obtained for different configurations. Analogous to Su-Schrieffer-Heeger (SSH) model in electronic systems, topological edge plasmon modes emerge when two periodic graphene sheet arrays with different Zak phases are connected. Interestingly, the dispersion of these topological edge modes is the same as that in the monolayer graphene and is invariant as the geometric parameters of the structure such as the separation and period change. These plasmonic edge states in multilayer graphene systems can be further tuned by electrical gating or chemical doping. PMID:26368137

Given a directed graph, a natural topology is defined and relationships between standard topological properties and graph theoretical concepts are studied. In particular, the properties of connectivity and separatedness are investigated. A metric is introduced which is shown to be related to separatedness. The topological notions of continuity and homeomorphism. A class of maps is studied which preserve both graph and topological properties. Applications involving strong maps and contractions are also presented.

Granular matter at the jamming transition is poised on the brink of mechanical stability, and hence it is possible that these random systems have topologically protected surface phonons. Studying two model systems for jammed matter, we find states that exhibit distinct mechanical topological classes, protected surface modes, and ubiquitous Weyl points. The detailed statistics of the boundary modes shed surprising light on the properties of the jamming critical point and help inform a common theoretical description of the detailed features of the transition. PMID:27345616

The problem of geometric symmetries in the intrinsic frame of a many-body system (nucleus) is considered. An importance of symmetrization group notion is discussed. Ageneral structure of the intrinsic symmetry group structure is determined.

For any topological space X let C(X) be the realization of the singular cubical set of X; let * be the topological space consisting of one point. In [1] Antolini proves, as a corollary to a general theorem about cubical sets, that C(X) and X×C(*) are homotopy equivalent, provided X is a CW-complex. In this note we give a short geometric proof that for any topological space X there is a natural weak homotopy equivalence between C(X) and X×C(*).

Emerging high-bandwidth, low-latency network technology has made network-based architectures both feasible and potentially desirable for use in satellite payload architectures. The selection of network topology is a critical component when developing these multi-node or multi-point architectures. This study examines network topologies and their effect on overall network performance. Numerous topologies were reviewed against a number of performance, reliability, and cost metrics. This document identifies a handful of good network topologies for satellite applications and the metrics used to justify them as such. Since often multiple topologies will meet the requirements of the satellite payload architecture under development, the choice of network topology is not easy, and in the end the choice of topology is influenced by both the design characteristics and requirements of the overall system and the experience of the developer.

Topology is familiar mostly from mathematics, but also natural sciences have found its concepts useful. Those concepts have been used to explain several natural phenomena in biology and physics, and they are particularly relevant for the electronic structure description of topological insulators and graphene systems. Here, we introduce topologically distinct graphene forms - graphene spirals - and employ density-functional theory to investigate their geometric and electronic properties. We found that the spiral topology gives rise to an intrinsic Rashba spin-orbit splitting. Through a Hamiltonian constrained by space curvature, graphene spirals have topologically protected states due to time-reversal symmetry. In addition, we argue that the synthesis of such graphene spirals is feasible and can be achieved through advanced bottom-up experimental routes that we indicate in this work. PMID:23568379

Topological quantum computation is a promising technique to achieve large-scale, error-corrected computation. Quantum hardware is used to create a large, 3-dimensional lattice of entangled qubits while performing computation requires strategic measurement in accordance with a topological circuit specification. The specification is a geometric structure that defines encoded information and fault-tolerant operations. The compilation of a topological circuit is one important aspect of programming a quantum computer, another is the mapping of the topological circuit into the operations performed by the hardware. Each qubit has to be controlled, and measurement results are needed to propagate encoded quantum information from input to output. In this work, we introduce an algorithm for mapping an topological circuit to the operations needed by the physical hardware. We determine the control commands for each qubit in the computer and the relevant measurements that are needed to track information as it moves through the circuit. PMID:24722360

Topological quantum computation is a promising technique to achieve large-scale, error-corrected computation. Quantum hardware is used to create a large, 3-dimensional lattice of entangled qubits while performing computation requires strategic measurement in accordance with a topological circuit specification. The specification is a geometric structure that defines encoded information and fault-tolerant operations. The compilation of a topological circuit is one important aspect of programming a quantum computer, another is the mapping of the topological circuit into the operations performed by the hardware. Each qubit has to be controlled, and measurement results are needed to propagate encoded quantum information from input to output. In this work, we introduce an algorithm for mapping an topological circuit to the operations needed by the physical hardware. We determine the control commands for each qubit in the computer and the relevant measurements that are needed to track information as it moves through the circuit.

Non-uniform magnetic domains with non-trivial topology, such as vortices and skyrmions, are proposed as superior state variables for nonvolatile information storage. So far, the possibility of logic operations using topological objects has not been considered. Here, we demonstrate numerically that the topology of the system plays a significant role for its dynamics, using the example of vortex-antivortex pairs in a planar ferromagnetic film. Utilising the dynamical properties and geometrical confinement, direct logic communication between the topological memory carriers is realised. This way, no additional magnetic-to-electrical conversion is required. More importantly, the information carriers can spontaneously travel up to ~300 nm, for which no spin-polarised current is required. The derived logic scheme enables topological spintronics, which can be integrated into large-scale memory and logic networks capable of complex computations. PMID:26508375

A topologically non-trivial band structure appears in a hexagonal lattice if time-reversal symmetry is broken, as suggested by F. D. M. Haldane. He further pointed out that, in combination with broken inversion symmetry, this gives rise to a phase diagram containing topologically distinct phases, yet without the necessity of a magnetic field. Studying the band structure of a hexagonal lattice with broken time reversal symmetry induced by complex valued next-nearest neighbor couplings, he showed that the boundaries of the topologically different phases are gap opening-and-closing transitions at the Dirac points. Whilst a realization of this model in a material was hardly conceivable, it provided the conceptual basis for other topological insulators and the quantum spin Hall effect. Prospects to realize the model with cold atoms emerged by advances in generating effective magnetic fields for neutral atoms and the idea to employ time-dependent fields to break time-reversal symmetry in a hexagonal lattice. Here we report on the implementation of the Haldane model in a periodically driven honeycomb optical lattice and the characterization of the topological Bloch bands using non-interacting fermionic atoms. Modulating the position of the lattice sites along a circular trajectory generates complex next-nearest-neighbor tunneling and a gap opens at the Dirac points, which we measure using momentum-resolved inter-band transitions. In analogy to a Hall conductance we observe a characteristic displacements of the atomic cloud under a constant force. By additionally breaking the inversion-symmetry, we identify the closing of the gap at an individual Dirac point, associated with the transition between the topologically distinct phases, obtaining good agreement with the calculated phase diagram. Whilst the physics of the non-interacting system is determined by the single-particle band structure, as studied in this work, the cold atom systems is also suited to explore the

We introduce a quantum dot in topological insulator nanofilm as a bump at the surface of the nanofilm. Such a quantum dot can localize an electron if the size of the dot is large enough, ≳5 nm. The quantum dot in topological insulator nanofilm has states of two types, which belong to two ('conduction' and 'valence') bands of the topological insulator nanofilm. We study the energy spectra of such defined quantum dots. We also consider intraband and interband optical transitions within the dot. The optical transitions of the two types have the same selection rules. While the interband absorption spectra have multi-peak structure, each of the intraband spectra has one strong peak and a few weak high frequency satellites. PMID:24590177

The condensation of bosons can induce transitions between topological quantum field theories (TQFTs). This as been previously investigated through the formalism of Frobenius algebras and with the use of Vertex lifting coefficients. We discuss an alternative, algebraic approach to boson condensation in TQFTs that is physically motivated and computationally efficient. With a minimal set of assumptions, such as commutativity of the condensation with the fusion of anyons, we can prove a number of theorems linking boson condensation in TQFTs with algebra extensions in conformal field theories and with the problem of factorization of completely positive matrices over the positive integers. We propose an algorithm for obtaining a condensed theory fusion algebra and its modular matrices. For example, this formalism can be used to build multi-layer TQFTs which could be a starting point to build three-dimensional topologically ordered phases. Using this formalism, we also give examples of bosons that cannot undergo a condensation transition due to topological obstructions.

We define a refined topological vertex which depends in addition on a parameter, which physically corresponds to extending the self-dual graviphoton field strength to a more general configuration. Using this refined topological vertex we compute, using geometric engineering, a two-parameter (equivariant) instanton expansion of gauge theories which reproduce the results of Nekrasov.

A complex connection exists between the 3 dimensional topological state of DNA in living organisms and biological processes including gene expression, DNA replication, recombination and repair. A significant limitation in developing a detailed, quantitative understanding of this connection is due to a lack of rigorous methods to calculate statistical mechanical properties of DNA molecules with complex topologies, including supercoiling, looping and knotting. This dissertation's main focus is on developing such methods and applying them to realistic DNA and nucleoprotein models. In chapter 2, a method is presented to calculate free energies and J factors of protein mediated DNA loops by normal mode analysis (NMA). This method is similar to calculations performed previously but with several significant advances. We apply the method to the specific case of DNA looping mediated by Cre recombinase protein. J factors calculated by our method are compared to experimental measurements to extract geometric and elastic properties of the Cre-DNA synaptic complex. In particular, the results suggest the existence of a synaptic complex that is more flexible than previously expected and may be explained by a stable intermediate in the reaction pathway that deviates significantly from the planar crystal structure. Calculating free energies of DNA looping is difficult in general, especially when considering intermediate length scales such as plasmid sized DNA which may readily adopt multiple topological states. In chapter 3, a novel method is presented to obtain free energies of semiflexible biopolymers with fixed topologies and arbitrary ratios of contour length L to persistence length P. High accuracy is demonstrated by calculating free energies of specific DNA knots with L/P = 20 and L/P = 40, corresponding to DNA lengths of 3000 and 6000 base pairs, respectively. We then apply the method to study the free-energy landscape for a model of a synaptic nucleoprotein complex

surface spectrum can be computed from bulk quantities. Specifically, we present an analytic prescription for computing the edge dispersion E(k) of a tight-binding Dirac Hamiltonian terminated at an abrupt crystalline edge, based on the bulk Hamiltonian. The result is presented as a geometric formula, relating the existence of surface states as well as their energy dispersion to properties of the bulk Hamiltonian. We further prove the bulk-boundary correspondence for this specific class of systems, connecting the Chern number and the chiral edge modes for quantum Hall systems given in terms of Dirac Hamiltonians. In similar spirit, we examine the existence of Majorana zero modes in superconducting doped-TIs. We find that Majorana zero modes indeed appear but only if the doped Fermi energy is below a critical chemical potential. The critical doping is associated with a topological phase transition of vortex lines, which supports gapless excitations spanning their length. For weak pairing, the critical point is dependent on the non-abelian Berry phase of the bulk Fermi surface. Finally, we investigate the transport properties on the surfaces of TIs. While the surfaces of “strong topological insulators” - TIs with an odd number of Dirac cones in their surface spectrum - have been well studied in literature, studies of their counterpart “weak topological insulators” (WTIs) are meager, with conflicting claims. Because WTIs have an even number of Dirac cones in their surface spectrum, they are thought to be unstable to disorder, which leads to an insulating surface. Here we argue that the presence of disorder alone will not localize the surface states, rather, presence of a time-reversal symmetric mass term is required for localization. Through numerical simulations, we show that in the absence of the mass term the surface always flow to a stable metallic phase and the conductivity obeys a one-parameter scaling relation, just as in the

Topologically nontrivial field excitations, including solitonic, linked, and knotted structures, play important roles in physical systems ranging from classical fluids and liquid crystals, to electromagnetism, classic, and quantum field theories. These excitations can appear spontaneously during symmetry-breaking phase transitions. For example, in cosmological theories, cosmic strings may have formed knotted configurations influencing the Early Universe development, whereas in liquid crystals transient tangled defect lines were observed during isotropic-nematic transitions, eventually relaxing to defect-free states. Knotted and solitonic fields and defects were also obtained using optical manipulation, complex-shaped colloids, and frustrated cholesterics. Here we use confinement of nematic liquid crystal by closed surfaces with varied genus and perpendicular boundary conditions for a robust control of appearance and stability of such field excitations. Theoretical modeling and experiments reveal structure of defect lines as a function of the surface topology and material and geometric parameters, establishing a robust means of controlling solitonic, knotted, linked, and other field excitations. PMID:25369931

Topologically nontrivial field excitations, including solitonic, linked, and knotted structures, play important roles in physical systems ranging from classical fluids and liquid crystals, to electromagnetism, classic, and quantum field theories. These excitations can appear spontaneously during symmetry-breaking phase transitions. For example, in cosmological theories, cosmic strings may have formed knotted configurations influencing the Early Universe development, whereas in liquid crystals transient tangled defect lines were observed during isotropic–nematic transitions, eventually relaxing to defect-free states. Knotted and solitonic fields and defects were also obtained using optical manipulation, complex-shaped colloids, and frustrated cholesterics. Here we use confinement of nematic liquid crystal by closed surfaces with varied genus and perpendicular boundary conditions for a robust control of appearance and stability of such field excitations. Theoretical modeling and experiments reveal structure of defect lines as a function of the surface topology and material and geometric parameters, establishing a robust means of controlling solitonic, knotted, linked, and other field excitations. PMID:25369931

Background Understanding how mesenchymal cells arise from epithelial cells could have a strong impact in unveiling mechanisms of epithelial cell plasticity underlying kidney regeneration and repair. In primary human tubular epithelial cells (HUTEC) under different TGFβ1 concentrations we had observed epithelial-to-mesenchymal transition (EMT) but not epithelial-myofibroblast transdifferentiation. We hypothesized that the process triggered by TGFβ1 could be a dedifferentiation event. The purpose of this study is to comprehensively delineate genetic programs associated with TGFβ1-driven EMT in our in vitro model using gene expression profile on large-scale oligonucleotide microarrays. Results In HUTEC under TGFβ1 stimulus, 977 genes were found differentially expressed. Thirty genes were identified whose expression depended directly on TGFβ1 concentration. By mapping the differentially expressed genes in the Human Interactome Map using Cytoscape software, we identified a single scale-free network consisting of 2630 interacting proteins and containing 449 differentially expressed proteins. We identified 27 hub proteins in the interactome with more than 29 edges incident on them and encoded by differentially expressed genes. The Gene Ontology analysis showed an excess of up-regulated proteins involved in biological processes, such as "morphogenesis", "cell fate determination" and "regulation of development", and the most up-regulated genes belonged to these categories. In addition, 267 genes were mapped to the KEGG pathways and 14 pathways with more than nine differentially expressed genes were identified. In our model, Smad signaling was not the TGFβ1 action effector; instead, the engagement of RAS/MAPK signaling pathway seems mainly to regulate genes involved in the cell cycle and proliferation/apoptosis. Conclusion Our present findings support the hypothesis that context-dependent EMT generated in our model by TGFβ1 might be the outcome of a dedifferentiation

We propose an alternative formulation of tachyon inflation using the geometrical tachyon arising from the time dependent motion of a BPS D3-brane in the background geometry due to k parallel NS5-branes arranged around a ring of radius R. Because of the fact that the mass of this geometrical tachyon field is {radical}(2/k) times smaller than the corresponding open-string tachyon mass, we find that the slow-roll conditions for inflation and the number of e-foldings can be satisfied in a manner that is consistent with an effective 4-dimensional model and with a perturbative string coupling. We also show that the metric perturbations produced at the end of inflation can be sufficiently small and do not lead to the inconsistencies that plague the open-string tachyon models. Finally we argue for the existence of a minimum of the geometrical tachyon potential which could give rise to a traditional reheating mechanism.

We investigate the topological structure of the subgraphs of dictionary graphs constructed from WordNet and Moby thesaurus data. In the process of learning a foreign language, the learner knows only a subset of all words of the language, corresponding to a subgraph of a dictionary graph. When this subgraph grows with time, its topological properties change. We introduce the notion of the pseudocore and argue that the growth of the vocabulary roughly follows decreasing pseudocore numbers—that is, one first learns words with a high pseudocore number followed by smaller pseudocores. We also propose an alternative strategy for vocabulary growth, involving decreasing core numbers as opposed to pseudocore numbers. We find that as the core or pseudocore grows in size, the clustering coefficient first decreases, then reaches a minimum and starts increasing again. The minimum occurs when the vocabulary reaches a size between 103 and 104. A simple model exhibiting similar behavior is proposed. The model is based on a generalized geometric random graph. Possible implications for language learning are discussed.

The performance characteristics are discussed of certain algebraic geometric codes. Algebraic geometric codes have good minimum distance properties. On many channels they outperform other comparable block codes; therefore, one would expect them eventually to replace some of the block codes used in communications systems. It is suggested that it is unlikely that they will become useful substitutes for the Reed-Solomon codes used by the Deep Space Network in the near future. However, they may be applicable to systems where the signal to noise ratio is sufficiently high so that block codes would be more suitable than convolutional or concatenated codes.

We investigate the geometry of one-norm geometric quantum discord and present a geometric interpretation of one-norm geometric quantum discord for a class of two-qubit states. It is found that one-norm geometric quantum discord has geometric behavior different from that described in Lang and Caves (Phys Rev Lett 105:150501, 2010), Li et al. (Phys Rev A 83:022321, 2011) and Yao et al. (Phys Lett A 376:358-364, 2012). We also compare the dynamics of the one-norm geometric quantum discord and other measures of quantum correlations under correlated noise. It is shown that different decoherent channels bring different influences to quantum correlations measured by concurrence, entropic quantum discord and geometric quantum discord, which depend on the memory parameter and decoherence parameter. We lay emphasis on the behaviors such as entanglement sudden death and sudden transition of quantum discord. Finally, we study the dynamical behavior of one-norm geometric quantum discord in one-dimensional anisotropic XXZ model by utilizing the quantum renormalization group method. It is shown that the one-norm geometric quantum discord demonstrates quantum phase transition through renormalization group approach.

We demonstrate the existence of topological superconductors (SCs) protected by mirror and time-reversal symmetries. D-dimensional (D=1, 2, 3) crystalline SCs are characterized by 2D-1 independent integer topological invariants, which take the form of mirror Berry phases. These invariants determine the distribution of Majorana modes on a mirror symmetric boundary. The parity of total mirror Berry phase is the Z2 index of a class DIII SC, implying that a DIII topological SC with a mirror line must also be a topological mirror SC but not vice versa and that a DIII SC with a mirror plane is always time-reversal trivial but can be mirror topological. We introduce representative models and suggest experimental signatures in feasible systems. Advances in quantum computing, the case for nodal SCs, the case for class D, and topological SCs protected by rotational symmetries are pointed out.

Choosing a multiprocessor interconnection topology may depend on high-level considerations, such as the intended application domain and the expected number of processors. It certainly depends on low-level implementation details, such as packaging and communications protocols. The authors first use rough measures of cost and performance to characterize several topologies. They then examine how implementation details can affect the realizable performance of a topology.

Topologically protected states can arise in electronic systems with broken time-reversal symmetry. We present a classical mechanical model for a solid in which broken time-reversal symmetry gives rise to topologically protected edge-modes, analogous to the edge modes in the quantum Hall effect. We will discuss numerical and experimental observations of these chiral edge-modes, their topological characterization, robustness and broader phenomenology.

This paper presents a highly automated hexahedral grid generator based on extensive geometrical and solid modeling operations developed in response to a vision of a designer-driven one day turnaround CFD process which implies a designer-driven one hour grid generation process.

Designed for a broad audience, including educators, camp directors, afterschool coordinators, and preservice teachers, this investigation aims to help individuals experience mathematics in unconventional and exciting ways by engaging them in the physical activity of building geometric shapes using ropes. Through this engagement, the author…

Children possess a genuine curiosity for exploring the natural world around them. One third grade teacher capitalized on this inherent trait by leading her students on "A Geometric Scavenger Hunt." The four-lesson inquiry investigation described in this article integrates mathematics and science. Among the students' discoveries was the fact that…

Three activities are presented to assess the level of students' geometric understanding according to van Hiele learning model. The activities--Descriptions, Minimum Properties, and Class Inclusion--are applied to the example of classifying quadrilaterals as squares, rectangles, rhombi, or parallelograms. Implications of this assessment are…

Quantification of subsurface model reliability is mathematically and technically demanding as there are many different sources of uncertainty and some of the factors can be assessed merely in a subjective way. For many practical applications in industry or risk assessment (e. g. geothermal drilling) a quantitative estimation of possible geometric variations in depth unit is preferred over relative numbers because of cost calculations for different scenarios. The talk gives an overview of several factors that affect the geometry of structural subsurface models that are based upon typical geological survey organization (GSO) data like geological maps, borehole data and conceptually driven construction of subsurface elements (e. g. fault network). Within the context of the trans-European project "GeoMol" uncertainty analysis has to be very pragmatic also because of different data rights, data policies and modelling software between the project partners. In a case study a two-step evaluation methodology for geometric subsurface model uncertainty is being developed. In a first step several models of the same volume of interest have been calculated by omitting successively more and more input data types (seismic constraints, fault network, outcrop data). The positions of the various horizon surfaces are then compared. The procedure is equivalent to comparing data of various levels of detail and therefore structural complexity. This gives a measure of the structural significance of each data set in space and as a consequence areas of geometric complexity are identified. These areas are usually very data sensitive hence geometric variability in between individual data points in these areas is higher than in areas of low structural complexity. Instead of calculating a multitude of different models by varying some input data or parameters as it is done by Monte-Carlo-simulations, the aim of the second step of the evaluation procedure (which is part of the ongoing work) is to

We predict the existence of a topological superradiant state in a two-component degenerate Fermi gas in a cavity. The superradiant light generation in the transversely driven cavity mode induces a cavity-assisted spin-orbit coupling and opens a bulk gap at half filling. This mechanism can simultaneously drive a topological phase transition in the system, yielding a topological superradiant state. We map out the steady-state phase diagram in the presence of an effective Zeeman field, and identify a critical tetracritical point beyond which the topological and the conventional superraidiant phase boundaries separate. The topological phase transition can be detected from its signatures in either the momentum distribution of the atoms or the variation of the cavity photon occupation due to the nontrivial feedback of the atoms on the cavity field. PMID:26252692

We predict the existence of a topological superradiant state in a two-component degenerate Fermi gas in a cavity. The superradiant light generation in the transversely driven cavity mode induces a cavity-assisted spin-orbit coupling and opens a bulk gap at half filling. This mechanism can simultaneously drive a topological phase transition in the system, yielding a topological superradiant state. We map out the steady-state phase diagram in the presence of an effective Zeeman field, and identify a critical tetracritical point beyond which the topological and the conventional superraidiant phase boundaries separate. The topological phase transition can be detected from its signatures in either the momentum distribution of the atoms or the variation of the cavity photon occupation due to the nontrivial feedback of the atoms on the cavity field.

Topological invariants built from the periodic Bloch functions characterize new phases of matter, such as topological insulators and topological superconductors. The most important topological invariant is the Chern number that explains the quantized conductance of the quantum Hall effect. Here we provide a general result for the superfluid weight Ds of a multiband superconductor that is applicable to topologically nontrivial bands with nonzero Chern number C. We find that the integral over the Brillouin-zone of the quantum metric, an invariant calculated from the Bloch functions, gives the superfluid weight in a flat band, with the bound Ds⩾|C|. Thus, even a flat band can carry finite superfluid current, provided the Chern number is nonzero. As an example, we provide Ds for the time-reversal invariant attractive Harper–Hubbard model that can be experimentally tested in ultracold gases. In general, our results establish that a topologically nontrivial flat band is a promising concept for increasing the critical temperature of the superconducting transition. PMID:26586543

Explanation of the quantization of the Hall conductance at low temperatures in strong magnetic field is one of the greatest accomplishments of theoretical physics of the end of the 20th century. Since the publication of the Laughlin's charge pumping argument condensed matter theorists have come a long way to topological insulators, classification of noninteracting (and sometimes interacting) topological phases of matter, non-abelian statistics, Majorana zero modes in topological superconductors and topological quantum computation---the framework for "error-free'' quantum computation. While topology was very important in these developments, geometry has largely been neglected. We explore the role of space-time symmetries in topological phases of matter. Such symmetries are responsible for the conservation of energy, momentum and angular momentum. We will show that if these symmetries are maintained (at least on average) then in addition to Hall conductance there are other, in principle, measurable transport coefficients that are quantized and sensitive to topological phase transition. Among these coefficients are non-dissipative viscosity of quantum fluids, known as Hall viscosity; thermal Hall conductance, and a recently discovered coefficient---orbital spin variance. All of these coefficients can be computed as linear responses to variations of geometry of a physical sample. We will show how to compute these coefficients for a variety of abelian and non-abelian quantum Hall states using various analytical tools: from RPA-type perturbation theory to non-abelian Chern-Simons-Witten effective topological quantum field theory. We will explain how non-Riemannian geometry known as Newton-Cartan (NC) geometry arises in the computation of momentum and energy transport in non-relativistic gapped systems. We use this geometry to derive a number of thermodynamic relations and stress the non-relativistic nature of condensed matter systems. NC geometry is also useful in the

Topologically ordered systems exhibit large-scale correlation in their ground states, which may be characterized by quantities such as topological entanglement entropy. We propose that the concept of irreducible many-body correlation (IMC), the correlation that cannot be implied by all local correlations, may also be used as a signature of topological order. In a topologically ordered system, we demonstrate that for a part of the system with holes, the reduced density matrix exhibits IMCs which become reducible when the holes are removed. The appearance of these IMCs then represents a key feature of topological phase. We analyze the many-body correlation structures in the ground state of the toric code model in external magnetic fields, and show that the topological phase transition is signaled by the IMCs.

It has been proposed that adding disorder to a topologically trivial mercury telluride/cadmium telluride (HgTe/CdTe) quantum well can induce a transition to a topologically nontrivial state. The resulting state was termed topological Anderson insulator and was found in computer simulations of the Bernevig-Hughes-Zhang model. Here, we show that the topological Anderson insulator is a more universal phenomenon and also appears in the Kane-Mele model of topological insulators on a honeycomb lattice. We numerically investigate the interplay of the relevant parameters, and establish the parameter range in which the topological Anderson insulator exists. A staggered sublattice potential turns out to be a necessary condition for the transition to the topological Anderson insulator. For weak enough disorder, a calculation based on the lowest-order Born approximation reproduces quantitatively the numerical data. Our results thus considerably increase the number of candidate materials for the topological Anderson insulator phase. PMID:27045779

It has been proposed that adding disorder to a topologically trivial mercury telluride/cadmium telluride (HgTe/CdTe) quantum well can induce a transition to a topologically nontrivial state. The resulting state was termed topological Anderson insulator and was found in computer simulations of the Bernevig-Hughes-Zhang model. Here, we show that the topological Anderson insulator is a more universal phenomenon and also appears in the Kane-Mele model of topological insulators on a honeycomb lattice. We numerically investigate the interplay of the relevant parameters, and establish the parameter range in which the topological Anderson insulator exists. A staggered sublattice potential turns out to be a necessary condition for the transition to the topological Anderson insulator. For weak enough disorder, a calculation based on the lowest-order Born approximation reproduces quantitatively the numerical data. Our results thus considerably increase the number of candidate materials for the topological Anderson insulator phase. PMID:27045779